Abstract
A systematic survey of the theory of linear evolution equations in Banach spaces, reviewed in the period 1968–1982 in Ref. Zh. Matematika, is presented.
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Literature cited
L. Sh. Abdulkerimov, “Regularization of improper problems for evolution equations in a Banach space,” Uch. Zap. Azerb. Univ. Ser. Fiz.-Mat. Nauk, No. 1, 32–36 (1977).
A. B. Aliev, “Almost-periodic solutions of linear differential equations in a Banach space,” Izv. Akad. Nauk AzSSR, Ser. Fiz.-Tekh. Mat. Nauk, No. 2, 29–34 (1975).
R. G. Aliev, “Differential equations in a Banach space whose solutions decrease faster than an exponential,” Vestn. Mosk. Univ. Mat., Mekh., No. 5, 3–7 (1974).
V. P. Anosov and P. E. Sobolevskii, “Coercive solvability of parabolic equations,” Mat. Zametki,11, No. 4, 409–419 (1972).
S. A. Atanbaev, “Regularization of evolution equations,” in: Questions of Mathematics and Applied Mathematics [in Russian], Alma-Ata (1977), pp. 19–22.
A. V. Babin and M. I. Vishik, “Attractors of the Navier-Stokes system and parabolic equations and estimates of their dimension,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,115, 3–15 (1982).
A. V. Babin and M. I. Vishik, “Existence and estimate of the dimension of attractors of quasilinear parabolic equations and the Navier-Stokes system,” Usp. Mat. Nauk,37, No.3, 173–174 (1982).
A. V. Babin and M. I. Vishik, “Attractors of quasilinear parabolic equations,” Dokl. Akad. Nauk SSSR,264, No. 4, 780–784 (1982).
N. Yu. Bakaev, “Semigroups of operators and differential equations in a Banach space,” Dokl. Akad. Nauk SSSR,258, No. 3, 521–523 (1981).
N. Yu. Bakaev and R. P. Tarasov, “Semigroups and a method of stable solution of Abel's equation,” Sib. Mat. Zh.,19, No. 1, 3–9 (1978).
A. B. Bakushinskii, “Difference schemes for the solution of an improper abstract Cauchy problem,” Differents. Uravn.,7, No. 10, 1876–1885 (1971).
A. B. Bakushinskii, “Solution by difference methods of an improper Cauchy problem for a second-order abstract differential equation,” Differents. Uravn.,8, No. 5, 881–890 (1972).
A. B. Bakushinskii, “Difference methods for solving improper Cauchy problems for evolution equations in a complex B-space,” Differents. Uravn.,8, No. 9, 1661–1668 (1972).
A. B. Bakushinskii, “Stabilization of solutions of certain abstract differential equations in Hilbert and Banach spaces,” in: Questions of Applied Mathematics [in Russian], Irkutsk (1975), pp. 127–139.
M. K. Balaev, “Propriety of a Cauchy problem for differential-operator equations of arbitrary order of parabolic type,” Izv. Akad. Nauk AzSSR, Ser. Fiz.-Tekh. Mat. Nauk, No. 5, 25–31 (1976).
Yu. Ya. Belov, “Systems of linear differential equations in Hilbert space,” Chisl. Metody Mekh. Splosh. Sredy (Novosibirsk),7, No. 3, 13–29 (1976).
Yu. Ya. Belov, “System of nonlinear operator equations in Banach space,” Dokl. Akad. Nauk SSSR,243, No. 3, 557–560 (1978).
Yu. Ya. Belov and E. G. Savateev, “Systems of equations with monotone operators,” in: Proper Boundary Problems for Nonclassical Equations of Mathematical Physics [in Russian], Novosibirsk (1981), pp. 28–30.
Yu. Ya. Belov and N. N. Yanenko, “A class of nonlocal nonlinear differential equations in a Banach space,” Dokl. Akad. Nauk SSSR,252, No. 6, 1292–1296 (1980).
Yu. Ya. Belov and N. N. Yanenko, “Nonlocal nonlinear differential equations in a Banach space,” Chisl. Metody Mekh. Splosh. Sredy (Novosibirsk),10, No. 6, 5–26 (1979).
Yu. Ya. Belov and N. N. Yanenko, “Cauchy problem for a pseudoparabolic equation in a Banach space,” Chisl. Metody Mekh. Splosh. Sredy (Novosibirsk),11, No. 7, 12–22 (1980).
Yu. Ya. Belov and N. N. Yanenko, “A system of differential equations in a Banach space,” Dokl. Akad. Nauk SSSR,263, No. 3, 526–529 (1982).
A. G. Belyi and Yu. A. Semenov, “Kato's inequality and semigroup product formulas,” Funkts. Anal. Prilozhen.,9, No. 4, 59–60 (1975).
G. M. Vainikko and M. Shlapikiene, “A theorem of S. G. Krein on perturbations of operators generating analytic semigroups,” Uch. Zap. Tartus. Univ., No. 281, 186–189 (1971).
V. V. Vasil'ev, “Coercive solvability of abstract parabolic equations with constant operator,” Differents. Uravn.,14, No. 8, 1507–1510 (1978).
N. I. Gavrishova, “Multiplicative theorem for nonlinear evolution systems,” Kiev Politekh. Inst., Kiev (1982).
Kh. Gaevskii, K. Gröger, and K. Zakharias, Nonlinear Operator Equations and Operator Differential Equations [Russian translation], Mir, Moscow (1978).
V. A. Galaktionov, “Conditions for the absence of global solutions of a class of quasilinear parabolic equations,” Zh. Vychisl. Mat. Mat. Fiz.,22, No. 2, 322–338 (1982).
R. Glovinski, J.-L. Lions, and R. Tremoller, Numerical Investigation of Variational Inequalities [Russian translation], Mir, Moscow (1979).
L. A. Groza, “Asymptotic solutions of linear differential equations in a Banach space containing an unbounded operator,” Differents. Uravn.,6, No. 2, 289–297 (1970).
Yu. L. Daletskii, “Self-adjointness and maximal dissipativeness of differential operators for functions of an infinite-dimensional argument,” Dokl. Akad. Nauk SSSR,227, No. 4, 784–787 (1976).
Yu. L. Daletskii and E. A. Fadeeva, “Hyperbolic equations with operator coefficients and ultraparabolic systems,” Ukr. Mat. Zh.,24, No. 1, 92–95 (1972).
Yu. L. Daletskii and E. A. Fadeeva, “Hyperbolic equations with variable operator coefficients,” Differents. Uravn.,12, No. 5, 881–891 (1976).
N. Dunford and J. T. Schwartz, Linear Operators. Pt. 1. General Theory, Wiley (1958).
N. Dunford and J. T. Schwartz, Linear Operators. Pt. 3. Spectral Operators, Wiley (1971).
Yu. A. Dubinskii, “Nonlinear elliptic and parabolic equations,” in: Contemporary Problems of Mathematics [in Russian], Vol. 9, Itogi Nauki i Tekh. VINITI AN SSSR, Moscow (1976), pp. 5–130.
S. V. D'yachenko, “Semigroups of generalized almost-negative type and stabilization of solutions of differential equations in a Banach space,” in: Differential Equations and Their Applications [in Russian], No. 3, Dnepropetrovsk (1975), pp. 82–87.
S. V. D'yachenko, “Semigroups of almost-negative type and their applications,” Dokl. Akad. Nauk SSSR,229, No. 6, 1306–1309 (1976).
S. V. D'yachenko, “Asymptotically stable evolution operators,” in: Differential Equations and Their Applications [in Russian], Dnepropetrovsk (1976), pp. 44–50.
S. V. D'yachenko, “Behavior of semigroups at infinity,” in: Differential Equations and Their Applications [in Russian], Dnepropetrovsk (1976), pp. 50–59.
S. V. D'yachenko, “Asymptotic stability of semigroups with strictly dissipative generating operator,” Mat. Zametki,28, No. 1, 75–78 (1980).
G. Duveau and J.-L. Lions, Inequalities in Mathematics and Physics [Russian translation], Nauka, Moscow (1980).
I. E. Egorov, “Nonlinear degeneration of a first-order operator equation,” in: Proper Boundary Problems for Nonclassical Equations of Mathematical Physics [in Russian], Novosibirsk (1980), pp. 61–68.
T. Kh. Enikeeva, “Sum of complete infinitesimal operators with common domain of definition,” Tr. Mosk. Inst. Elektron. Mashinostr., No. 15, 113–120 (1971).
V. V. Zhikov, “Proof of Favard's theorem on the existence of an almost-periodic solution in the case of an arbitrary Banach space,” Mat. Zametki,23, No. 1, 121–126 (1978).
V. V. Zhikov and B. M. Levitan, “Favard theory,” Usp. Mat. Nauk,32, No. 2, 123–171 (1977).
P. P. Zabreiko and A. V. Zafievskii, “A class of semigroups,” Dokl. Akad. Nauk SSSR,189, No. 5, 934–937 (1969).
A. V. Zafievskii, “Semigroups having singularities at zero which are summable with a power weight,” Dokl. Akad. Nauk SSSR,195, No. 1, 24–27 (1970).
A. V. Zafievskii, “Analytic semigroups with singularities,” Tr. Mat. Fak. Voronezh. Univ., No. 1, 206–210 (1970).
A. V. Zafievskii, “New classes of semigroups,” Vestn. Yaroslav. Univ., No. 8, 53–77 (1974).
A. V. Zafievskii, “Abstract Cauchy problem,” Vestn. Yaroslav. Univ., No. 12, 46–64 (1975).
I. S. Zeinalov, “Improper problem for an abstract parabolic equation in a Banach space,” Dokl. Akad. Nauk AzSSR,37, No. 9, 7–9 (1981).
S. P. Zubova and K. I. Chernyshov, “Linear differential equation with Fredholm operator for derivative,” Differents. Uravn. Primen. (Vilnius), No. 14, 21–39 (1976).
S. P. Zubova and K. I. Chernyshov, “Differential equations in a Banach space, unsolvable for the derivative,” in: Methods of Solution of Operator Equations [in Russian], Voronezh (1978), pp. 62–65.
K. Yosida, Functional Analysis, Springer-Verlag (1974).
A. D. Iskenderov and R. G. Tagiev, “Inverse problem on determining right sides of evolution equations in a Banach space,” Nauch. Tr. Azerb. Univ. Vopr. Prikl. Mat. Kibern., No. 1, 51–56 (1979).
B. G. Karasik, “Regularization of an improper Cauchy problem for differential-operator equations of arbitrary order,” Izv. Akad. Nauk AzSSR, Ser. Fiz.-Tekh. Mat. Nauk, No. 6, 9–14 (1976).
T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag (1966).
N. V. Kislov, “Projection theorem and its application to inhomogeneous boundary problems,” Dokl. Akad. Nauk SSSR,265, No. 1, 31–34 (1982).
V. S. Korolyuk and A. F. Turbin, “Method of use of perturbations on the spectrum of linear operators and some applications of it,” in: Problems of the Asymptotic Theory of Nonlinear Oscillations [in Russian], Kiev (1977), pp. 107–114.
V. S. Korolyuk and A. F. Turbin, Mathematical Foundations of Phase Amalgamation of Complex Systems [in Russian], Naukova Dumka, Kiev (1978).
V. S. Korolyuk and A. F. Turbin, Processes of Markov Restoration in Problems of Reliability of Systems [in Russian], Naukova Dumka, Kiev (1982).
S. G. Krein, Linear Differential Equations in Banach Space, Amer. Math. Soc. (1972).
S. G. Krein and I. M. Kulikov, “Maxwell-Leontovich operator,” Differents. Uravn.,5, No. 7, 1275–1282 (1969).
S. G. Krein, G. I. Laptev, and G. A. Tsvetkova, “Hadamard property of the Cauchy problem for an evolution equation,” Dokl. Akad. Nauk SSSR,192, No. 5, 980–983 (1970).
S. G. Krein and Yu. B. Savchenko, “Exponential dichotomy for partial differential equations,” Differents. Uravn.,8, No. 5, 835–844 (1972).
S. B. Kuksin, “Application of monotone semigroups to the theory of ideal-elastoplasticity,” Usp. Mat. Nauk,37, No. 5, 189–190 (1982).
A. N. Kulikov, “Smooth invariant manifolds of a semigroup of nonlinear operators in a Banach space,” in: Studies on Stability and the Theory of Oscillations [in Russian], Yaroslavl' (1976), pp. 114–129.
V. V. Kutuzov, “Solvability of a mixed problem for a system of quasilinear first-order equations,” Voronezh Univ. (1977).
V. V. Kutuzov, “Classical solutions of the Hamilton-Jacobi equation,” Krasnoyar. Inst. Tsvet. Met., Krasnoyarsk (1980).
V. V. Kutuzov, “Existence of nonlinear semigroups for a class of locally dissipative operators,” Submitted to Sib. Mat. Zh., Sib. Otd. Akad. Nauk SSSR, Novosibirsk (1982).
V. V. Kutuzov, “Application of the theory of nonlinear semigroups of operators to the solvability of nonlinear parabolic initial-boundary problems,” Krasnoyar. Inst. Tsvet. Met., Krasnoyarsk (1982).
V. V. Kutuzov, “A class of semigroups of nonlinear operators in a Banach space,” in: Operator Methods in Nonlinear Analysis [in Russian], Voronezh (1982), pp. 69–75.
V. V. Kutuzov and G. I. Laptev, “Nonlinear monotone differential operators in spaces of continuous functions,” in: Methods of Solution of Operator Equations [in Russian], Voronezh (1978), pp. 72–76.
M. M. Lavrent'ev, “An equation of evolution type,” in: Some Problems of Computational and Applied Mathematics [in Russian], Nauka, Novosibirsk (1975), pp. 111–114.
M. M. Lavrent'ev and A. Kh. Amirov, “Conditional propriety of the Cauchy problem for a certain equation of evolution type,” Dokl. Akad. Nauk SSSR,227, No. 5, 1053–1055 (1976).
M. M. Lavrent'ev and A. Kh. Amirov, “A conditionally proper problem,” Dokl. Akad. Nauk SSSR,232, No. 4, 773–776 (1977).
M. M. Lavrent'ev and A. Kh. Amirov, “Conditional propriety of a Cauchy problem,” Funkts. Anal. Prilozhen.,11, No. 2, 80–82 (1977).
O. A. Ladyzhenskaya, “Finite-dimensionality of bounded invariant sets for the Navier-Stokes system and some other dissipative systems,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,115, 137–155 (1982).
O. A. Ladyzhenskaya, “Finite-dimensionality of bounded invariant sets for dissipative problems,” Dokl. Akad. Nauk SSSR,263, No. 4, 802–804 (1982).
G. I. Laptev, “Operator calculus of linear unbounded operators and semigroups,” Funkts. Anal. Prilozhen.,4, No. 4, 31–40 (1970).
G. I. Laptev, “Exponential solutions of the Cauchy problem with constant operator,” Differents. Uravn.,7, No. 2, 232–243 (1971).
G. I. Laptev, “Uniform propriety condition of the Cauchy problem for systems of equations,” Dokl. Akad. Nauk SSSR,220, No. 2, 281–284 (1975).
G. I. Laptev, “A topological principle in the theory of semigroups of linear operators,” Tr. NII Mat. Voronezh. Univ., No. 17, 91–93 (1975).
G. I. Laptev, “Monotone operators in spaces of continuous functions,” Tr. NII Mat. Voronezh. Univ., No. 20, 39–45 (1975).
R. Lattes and J.-L. Lions, Method of Quasi-Reversibility: Applications to Partial Differential Equations, Elsevier (1969).
B. M. Levitan and V. V. Zhikov, Almost-Periodic Functions and Differential Equations [in Russian], Moscow State Univ. (1978).
J.-L. Lions, Some Mehtods of Solution of Nonlinear Boundary Problems [Russian translation], Mir, Moscow (1972).
A. L. Likhtarnikov, “Test for absolute stability of nonlinear operator equations,” Izv. Akad. Nauk SSSR, Ser. Mat.,41, No. 5, 1064–1083 (1977).
A. L. Likhtarnikov and V. A. Yakubovich, “Frequency theorem for continuous one-parameter semigroups,” Izv. Akad. Nauk SSSR, Ser. Mat.,41, No. 4, 895–911 (1977).
A. L. Likhtarnikov and V. A. Yakubovich, “Frequency theorems and theorem on stabilization for unbounded operators,” Usp. Mat. Nauk,33, No. 2, 195–196 (1978).
Yu. I. Lyubich, “Classical and local Laplace transform in the abstract Cauchy problem,” Usp. Mat. Nauk,21, No. 3, 3–51 (1966).
Ya. D. Mamedov and P. E. Sobolevskii, “A theorem of E. Hille,” Dokl. Akad. Nauk Azerb. SSR,22, No. 7, 7–9 (1966).
I. Marek, “Asymptotic behavior of solutions of a homogeneous transport equation,” in: Partial Differential Equations [in Russian], Novosibirsk (1980), pp. 181–186.
J. E. Marsden and M. McCracken, The Hopf Bifurcation and Its Applications, Springer-Verlag (1976).
I. V. Mel'nikova, “Solution of the inverse Cauchy problem by the method of quasiinversion,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 6, 36–38 (1981).
S. M. Midzokhata, Theory of Partial Differential Equations [Russian translation], Mir, Moscow (1977).
G. N. Mil'shtein, “Exponential stability of positive semigroups in a linear topological space,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 9, 35–42 (1975).
G. N. Mil'shtein, “Exponential stability of positive semigroups in a linear topological space. II,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 10, 51–61 (1975).
L. Nirenberg, Lectures on Nonlinear Functional Analysis [Russian translation], Mir, Moscow (1977).
L. V. Ovsyannikov, “Nonlinear Cauchy problem in the scale of Banach spaces,” Dokl. Akad. Nauk SSSR,200, No. 4, 789–792 (1971).
L. V. Ovsyannikov, “Cauchy problem in the scale of Banach spaces of analytic functions,” in: Proceedings of the analytic functions,” in: Proceedings of the Symposium on the Mechanics of Continuous Media and Related Problems of Analysis, 1971 [in Russian], Vol. 2, Metsniereba, Tbilisi (1974), pp. 218–229.
L. V. Ovsyannikov, “Abstract form of the Cauchy-Kowalewsky theorem and its applications,” in: Partial Differential Equations [in Russian], Nauka, Novosibirsk (1980), pp. 88–94.
V. B. Osipov, “An equation in a Banach space with degenerate operator for derivative,” in: Volume of Papers of Graduate Students in Mathematics and Mechanics [in Russian], Voronezh Univ. (1969), pp. 42–47.
I. K. Osipova, “Perturbation of semigroups of contracting operators,” in: Research in Mathematics, Physics, Chemistry [in Russian], Privolzh. Kn. Izd-vo, Saratov (1973), pp. 66–79.
S. Okharu, “Nonlinear evolution equations,” Sugaku,30, No. 1, 55–67 (1978).
A. A. Pankov, “Boundedness and almost-periodicity in time of solutions of evolutional variational inequalities,” Izv. Akad. Nauk SSSR, Ser. Mat.,46, No. 2, 314–346 (1982).
A. A. Pankov, “Bounded and almost-periodic solutions of certain nonlinear evolution equations,” Usp. Mat. Nauk,37, No. 2, 223–224 (1982).
S. Piskarev, “Approximation of holomorphic semigroups,” Uch. Zap. Tartus. Univ., No. 492/24, 3–14 (1979).
Ya. D. Plotkin and A. F. Turbin, “Decomposition of singular perturbed analytic semigroups of operators,” Inst. Mat. Akad. Nauk Ukr. SSR, Preprint No. 19 (1978).
O. I. Prozorovskaya, “Quasianalyticity of solutions of a differential equation,” Tr. Sem. Funkts. Analizu. Voronezh. Univ., No. 9, 144–148 (1967).
O. I. Prozorovskaya, “Speed of convergence of a semigroup operator to the identity,” Tr. NII Mat. Voronezh. Univ., No. 1, 111–119 (1970).
L. N. Prokopenko, “Uniqueness of the solution of a problem for operator-differential equations,” Dokl. Akad. Nauk SSSR,148, No. 5, 1030–1033 (1963).
N. I. Radbel', “Initial manifold and dissipativeness of the Cauchy problem for the equation Ax′ (t) + Bx(t) = 0,” Differents. Uravn.,15, No. 6, 1142–1143 (1979).
M. C. Reed and B. Simon, Methods of Modern Mathematical Physics. Vol. 1. Functional Analysis, Academic Press (1972).
M. C. Reed and B. Simon, Methods of Modern Mathematical Physics. Vol. 2. Harmonic Analysis. Self-Adjointness, Academic Press.
M. C. Reed and B. Simon, Methods of Modern Mathematical Physics. Vol. 3. Scattering Theory, Academic Press.
M. C. Reed and B. Simon, Methods of Modern Mathematical Physics. Vol. 4. Analysis of Operators, Academic Press.
R. Richtmeyer, Principles of Contemporary Mathematical Physics [Russian translation], Mir, Moscow (1982).
A. G. Rutkas, “Cauchy problem for the equation Ax′(t) + Bx(t) = f(t),” Differents. Uravn.,11, No. 11, 1996–2010 (1975).
E. G. Savateev, “Evolutional variational inequality for a class of operators,” Dinam. Sploshn. Sredy (Novosibirsk), No. 51, 142–158 (1981).
Yu. B. Savchenko, “Homogeneous semiboundary problem for an equation in a Banach space,” Tr. Sem. Funkts. Anal. Voronezh. Univ., No. 10, 146–159 (1968).
Yu. B. Savchenko, “Solution of a homogeneous semiboundary problem on a half-line with the help of a singular integral equation,” in: Collection of Papers of Graduate Students in Mathematics and Mechanics [in Russian], Voronezh. Univ. (1969), pp. 47–55.
S. N. Samborskii, “Dependence on parameters of solutions of evolution equations,” Differents. Uravn.,13, No. 10, 1891–1893 (1977).
Yu. T. Sil'chenko, “Evolution equation with operator generating a nonanalytic semigroup,” Differents. Uravn.,15, No. 2, 363–366 (1979).
Yu. T. Sil'chenko and P. E. Sobolevskii, “A class of evolutional problems,” Voronezh. Univ., Voronezh (1977).
V. V. Smagin and P. E. Sobolevskii, “Comparison theorems for the norm of solutions of linear homogeneous differential equations in Hilbert spaces,” Differents. Uravn.,6, No. 11, 2005–2010 (1970).
T. I. Smagina, “Solvability of first-order differential equations with unbounded operator coefficients,” Voronezh. Univ., Voronezh (1977).
P. E. Sobolevskii, “Coerciveness inequalities for abstract parabolic equations,” Dokl. Akad. Nauk SSSR,157, No. 1, 52–55 (1964).
P. E. Sobolevskii, “Parabolic equations in spaces of means,” Dokl. Akad. Nauk SSSR,177, No. 2, 281–284 (1967).
P. E. Sobolevskii, “Differential equations with unbounded operators generating nonanalytic semigroups,” Dokl. Akad. Nauk SSSR,183, No. 2, 292–295 (1968).
P. E. Sobolevskii, “Fractional integration by parts,” Dokl. Akad. Nauk SSSR,183, No. 6, 1269–1272 (1968).
P. E. Sobolevskii, “A type of differential equation in a Banach space,” Differents. Uravn.,4, No. 12, 2278–2280 (1968).
P. E. Sobolevskii, “Differential equations of parabolic type in a Banach space,” in: Collection of Papers on Function Spaces and Operator Equations [in Russian], Voronezh (1970), pp. 95–122.
P. E. Sobolevsii, “Semigroups of growth α,” Dokl. Akad. Nauk SSSR,196, No. 3, 535–537 (1971).
P. E. Sobolevskii, “Properties of solutions of differential equations in fractional spaces,” Tr. NII Mat. Voronezh. Univ., No. 14, 68–74 (1974).
P. E. Sobolevskii, “Theory of semigroups and stability of difference schemes,” in: Theory of Operators in Function Spaces [in Russian], Novosibirsk (1977), pp. 304–337.
V. A. Solonnikov, “Estimates of solutions of a nonstationary Navier—Stokes system,” J. Sov. Math.,8, No. 4 (1977).
A. F. Turbin, “Regular approximations to solutions of singularly perturbed differential equations in Banach spaces,” Inst. Mat. Akad. Nauk Ukr. SSR, Preprint No. 7 (1979).
A. F. Turbin, “Limit theorems and asymptotic expansions for singularly perturbed semigroups of operators,” Inst. Mat. Akad. Nauk Ukr. SSR, Preprint No. 18, 13–41 (1980).
T. Usidzima, “Approximation of a semigroup and the method of finite elements,” Sugaku,32, No. 2, 133–148 (1980).
M. I. Khazan, “Nonlinear evolution equations in locally convex spaces,” Dokl. Akad. Nauk SSSR,212, No. 6, 1309–1312 (1973).
M. I. Khazan, “A theorem on perturbations of m-dissipative operators,” in: Investigations on the Theory of Differential and Difference Equations [in Russian], Riga (1974), pp. 115–122.
M. I. Khazan, “Differentiability of nonlinear evolution systems in nonreflexive Banach spaces,” in: Investigations on the Theory of Differential and Difference Equations [in Russian], Riga (1974), pp. 85–114.
M. I. Khazan, “Existence in the large of a continuous solution of an initial-boundary problem for a first-order quasilinear equation,” Differents. Uravn.,10, No. 8, 1478–1485 (1974).
M. I. Khazan, “Dissipativeness of abstract operators, generated by first-order quasilinear differential operators,” Latv. Mat. Ezhegod. (Riga), No. 16, 241–261 (1975).
M. I. Khazan, “Problems with unilateral boundary conditions for quasilinear elliptic and parabolic equations,” in: Investigations on the Theory of Differential and Difference Equations [in Russian], Latv. Univ. Riga (1976), pp. 131–160.
M. I. Khazan, “Differentiability of nonlinear semigroups and classical solvability of nonlinear boundary problems for the equation ϕ (iu t )=u xx ,” Dokl. Akad. Nauk SSSR,228, No. 4, 805–808 (1976).
M. I. Khazan, “Nonlinear evolution equations with quasidissipative operators,” in: Methods of Solution of Operator Equations [in Russian], Voronezh (1978), pp. 166–167.
M. I. Khazan, “New results on multiplicative formulas for nonlinear evolution equations,” in: Fifteenth Voronezh Winter Mathematics School [in Russian], Voronezh (1981), pp. 114–115.
M. I. Khazan, “Existence and approximation of solutions of nonlinear evolution equations,” Latv. Mat. Ezhegod. (Riga), No. 26, 114–131 (1982).
M. I. Khazan, “Nonlinear evolution equations with small parameter,” Preprint, Inst. Mat. Akad. Nauk Ukr. SSR, No. 50 (1981), pp. 25–29.
M. I. Khazan, “Nonlinear and quasilinear evolution equations: existence, uniqueness, and comparison of solutions: rate of convergence of difference method,” J. Sov. Math.,27, No. 2 (1984).
M. I. Khazan, “Comparison theorems for nonlinear evolution equations and their application to the investigation of the dependence of solutions of the equationu t =Δϕ(u) on ϕ and boundary conditions,” in: Problems of Mathematical Analysis [in Russian], Vol. 9, Leningrad (1984), pp. 242–264.
E. Hille and R. S. Phillips, Functional Analysis and Semigroups, Amer. Math. Soc., (1974).
S. B. Shikhov, Questions of the Mathematical Theory of Reactors. Linear Analysis [in Russian], Atomizdat, Moscow (1973).
É. A. Shteinvil', “Propriety of general boundary problems for parabolic equations,” Voronezh Univ. (1978).
É. A. Shteinvil', “Propriety on sets of smooth functions of general boundary problems for evolution equations,” Voronezh. Lesotekh. Inst., Voronezh (1979).
Yu. S. Éidel'man, “Two-point problem with parameter for a first-order differential equation with unbounded operator coefficient,” in: Fifteenth Voronezh Winter Mathematics School [in Russian], Voronezh (1981), pp. 133–134.
Yu. S. Éidel'man, “Solvability of a boundary problem for a differential equation in a Banach space with unbounded operator and unknown parameter,” Voronezh Univ. (1980).
S. Ya. Yakubov and M. K. Balaev, “Proper solvability of differential-operator equations on the whole line,” Dokl. Akad. Nauk SSSR,229, No. 3, 562–565 (1976).
S. Agmon and L. Nirenberg, “Properties of solutions of ordinary differential equations in Banach space,” Commun. Pure Appl. Math.,16, No. 2, 121–239 (1963).
S. Aizawa, “A semigroup treatment of the Hamilton-Jacobi equation in one space variable,” Hiroshima Math. J.,3, No. 2, 367–386 (1973).
S. Aizawa, “A semigroup treatment of the Hamilton-Jacobi equation in several space variables,” Hiroshima Math. J.,6, No. 1, 15–30 (1976).
N. D. Alikakos and R. Rostamian, “Lower bound estimates and separable solutions for homogeneous equations of evolution in Banach space,” J. Diff. Equat.,43, No. 3, 323–344 (1982).
N. D. Alikakos and R. Rostamian, “Gradient estimates for degenerate diffusion equations. II,” Proc. R. Soc. Edinburgh,A91, Nos. 3–4, 335–346 (1982).
M. Altman, “Nonlinear evolution equations in Banach spaces,” J. Integr. Equat.,4, No. 4, 307–322 (1982).
H. Attouch, “Équations d'évolution multivoques en dimension infinie,” C. R. Acad. Sci.,274, No. 17, A1289-A1291 (1972).
H. Attouch, “Convergence de fonctions convexes, des sous differentiels et semigroupes associes,” C. R. Acad. Sci.,284, No. 10, A539-A542 (1977).
H. Attouch, Ph. Benilan, A. Damlamian, and C. Picard, “Equations d'evolutions avec condition unilaterale,” C. R. Acad. Sci.,A279, No. 15, 607–609 (1974).
H. Attouch and A. Damlamian, “On multivalued evolution equations in Hilbert spaces,” Isr. J. Math.,12, No. 4, 373–390 (1972).
H. Attouch and A. Damlamian, “Problèmes d'évolution dans les Hilberts et applications,” J. Math. Pures Appl.,54, No. 1, 53–74 (1975).
H. Attouch and A. Damlamian, “Application des méthodes de convexité et monotonie à l'étude de certains équations quasilineaires,” Proc. R. Soc. Edinburgh,A79, Nos. 1–2, 107–129 (1977).
A. Baider and B. Cherkos, “Hypoelliptic infinitesimal generators,” SIAM J. Math. Anal.,8, No. 6, 971–977 (1977).
J.-B. Baillon, “Un théorème de type ergodique pour les contractions nonlinéaires dans un espace de Hilbert,” C. R. Acad. Sci.,280, No. 22, A1511-A1514 (1975).
J.-B. Baillon, “Quelques propriétés de convergence asymptotique pour les semigroupes de contractions impaires,” C. R. Acad. Sci.,283, No. 3, A75-A78 (1976).
J.-B. Baillon, “Un example concernant le comportement asymptotique de la solution du problème ∂u/∂t +∂ϕ(u)Э0,” J. Funct. Anal.,28, No. 3, 369–376 (1978).
J.-B. Baillon, “Generateurs et semigroupes dans les espaces de Banach uniformement lisses,” J. Funct. Anal.,29, No. 2, 199–213 (1978).
J.-B. Baillon, “Caractère borné de certains générateurs de semigroupes linéaires dans les espaces de Banach,” C. R. Acad. Sci.,AB 290, No. 16, A757–A760.
J.-B. Baillon, “Nonlinear ergodic theory in Banach spaces,” Delft Progr. Rept.,6, No. 2, 87–96 (1981).
J.-B. Baillon and H. Brezis, “Une remarque sur le comportement asymptotique des semigroupes non linéaires,” Houston J. Math.,2, No. 1, 5–7 (1976).
J.-B. Baillon, R. H. Bruck, and S. Reich, “On the asymptotic behavior of nonexpansive mappings and semigroups in Banach spaces,” Houston J. Math.,4, No. 1, 1–9 (1978).
M. Balabane and H. A. Emamirad, “Smooth distribution group and Schrödinger equation in LP(R n),” J. Math. Anal. Appl.,70, No. 1, 61–71 (1979).
J. M. Ball, “Continuity properties of nonlinear semigroups,” J. Funct. Anal.,17, No. 1, 91–103 (1974).
J. M. Ball, “Strongly continuous semigroups, weak solutions, and the variation of constants formula,” Proc. AMS,63, No. 2, 370–373 (1977).
J. M. Ball, “On the asymptotic behaviour of generalized processes, with applications to nonlinear evolution equations,” J. Diff. Equat.,27, No. 2, 224–265 (1978).
M. S. Baouendi and C. Goulaouic, “Remarks on the abstract form of nonlinear Cauchy-Kovalevsky theorems,” Commun. Part. Diff. Equat.,2, No. 11, 1151–1162 (1977).
P. Baras, “Compacite de l'opérateur f → u solution d'une équation non linéaire du/dt + Au Э f,” C. R. Acad. Sci.,AB286, No. 23, A1113–1116 (1978).
P. Baras, J.-C. Hassan, and L. Veron, “Compacité de l'operateur définissant la solution d'une équation d'évolution nonhomogène,” C. R. Acad. Sci.,284, No. 14, A799-A802 (1977).
V. Barbu, “Les semigroupes distributions differentiables,” C. R. Acad. Sci.,267, No. 23, A875-A878 (1968).
V. Barbu, “Sur la perturbation du générateur d'un semigroupe non linéaire de contraction,” C. R. Acad. Sci.,268, No. 25, A1544-A1547 (1969).
V. Barbu, “On the regularity of the weak solutions of abstract differential equations,” Osaka J. Math.,6, No. 1, 49–56 (1969).
V. Barbu, “Differentiable distribution semigroups,” Ann. Scuola Norm. Super. Pisa. Sci. Fis. Mat.,23, No. 3, 413–429 (1969).
V. Barbu, “Dissipative sets and nonlinear perturbed equations in Banach spaces,” Ann. Scuola Norm. Super. Pisa. Sci. Fis. Mat.,26, No. 2, 365–390 (1972).
V. Barbu, “Continuous perturbations of nonlinear m-accretive operators in Banach spaces,” Boll. Unione Mat. Ital.,6, No. 2, 270–278 (1972).
V. Barbu, “Regularity properties of some nonlinear evolution equations,” Rev. Roum. Math. Pures Appl.,18, No. 10, 1503–1514 (1973).
V. Barbu, “Convex control problems of Bolza in Hilbert spaces,” SIAM J. Contr.,13, No. 4, 754–771 (1975).
V. Barbu, “On the convex control problem of Bolza in Hilbert spaces,” SIAM J. Control,13, No. 5, 1062–1076 (1975).
V. Barbu, “Un théorème d'existence pour une équation doublement non linéaire dans un espace de Hilbert,” C. R. Acad. Sci.,285, No. 3, A107-A109 (1977).
V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Ed. Acad., Leyden, Nordhoff Int. Publ., Bucuresti (1976).
V. Barbu and G. Da Prato, “Global existence for the Hamilton-Jacobi equations in Hilbert space,” Ann. Scuol. Norm. Super. Pisa. Cl. Sci.,8, No. 2, 257–284 (1981).
E. Barone, “Su un problema di traffico automobilistico,” Boll. Unione Mat. Ital.,9, No. 2, 450–462 (1974).
H. Bart, “Periodic strongly continuous semigroups,” Ann. Mat. Pura Appl.,115, 311–318 (1977).
H. Bart and S. Goldberg, “Characterisations of almost periodic strongly continuous groups and semigroups,” Math. Ann.,236, No. 2, 105–116 (1978).
R. Beals, “On the abstract Cauchy problem,” J. Funct. Anal.,10, No. 3, 281–299 (1972).
R. Beals, “Semigroups and abstract Gevrey spaces,” J. Funct. Anal.,10, No. 3, 300–308 (1972).
R. Beals, “Laplace transform methods for evolution equations,” in: Boundary Value Problems of Linear Evolut. Partial Differential Equations. Proc. NATO Adv. Study Inst. Liege, 1976. Dordrecht-Boston (1977), pp. 1–26.
R. Beals, “An abstract treatment of some forward-backward problems of transport and scattering,” J. Funct. Anal.,34, No. 1, 1–20 (1979).
H. Beirão da Veiga, “Inhomogeneous evolution equations in Banach spaces with a bounded variation data,” Nonlinear Anal.: Theory, Meth. Appl.,3, No. 2, 249–259 (1979).
A. Belleni-Morante, Applied Semigroups and Evolution Equations, Oxford Univ. Press (1979).
C. D. Benchimol, “A note on weak stability of contraction semigroups,” SIAM J. Contr. Optim.,16, No. 3, 373–379 (1978).
C. D. Benchimol, “Feedback stabilizability in Hilbert spaces,” Appl. Math. Optim.,4, No. 3, 225–248 (1978).
Ph. Bénilan, “Une remarque sur la convergence des semigroupes nonlinéaires,” C. R. Acad. Sci.,272, No. 18, A1182-A1184 (1971).
Ph. Bénilan, “Solutions intégrales d'équations d'évolution dans un espace de Banach,” C. R. Acad. Sci.,274, No. 1, A47-A50 (1972).
Ph. Bénilan, “Equations d'évolution dans un espace de Banach quelconque et applications. Thèse Doct.-Sci. Math. Univ. Paris, Centre Orsay (1972).
Ph. Bénilan, “Opérateurs m-accrétifs hémicontinus dans un espace de Banach quelconque,” C. R. Acad. Sci.,A278, No. 16, 1029–1032 (1974).
Ph. Bénilan and H. Brezis, “Solutions faibles d'équations d'évolution dans les espaces de Hilbert,” Ann. Inst. Fourier,22, No. 2, 311–329 (1972).
Ph. Bénilan and F. Catte, “Équation d'évolution du type du/dt + maxAiu = f par la théorie des semigroupes non linéaires dans L∞,” C. R. Acad. Sci., Ser. 1,295, No. 7, 447–450 (1982).
Ph. Bénilan and J. I. Diaz, “Comparison of solutions of nonlinear evolution problems with different nonlinear terms,” Isr. J. Math.,42, No. 3, 242–257 (1982).
Ph. Bénilan and Ha Kisik, “Equation d'évolution du type du/dt +β∂ϕ(u)Э0 dans L∞(Ω),” C. R. Acad. Sci.,281, No. 22, A947-A950 (1975).
A. Beurling, “On analytic extension of semigroups of operators,” J. Funct. Anal.,6, No. 3, 387–400 (1970).
M. Biroli, “Sur les solutions bornées et presques périodiques des équations et inéquations d'évolution,” Ann. Mat. Pura Appl.,93, 1–79 (1972).
A. de Bivar-Weinholtz, “Sur l'opérateur de Schrödinger avec potentiel singulier magnétique, dans un ouvert arbitraire de RN,” C. R. Acad. Sci., Ser. 1,294, No. 6, 213–216 (1982).
A. de Bivar-Weinholtz and R. Piraux, “Formule de Trotter pour l'opérateur de Schrödinger avec un potentiel singulier complexe,” C. R. Acad. Sci.,AB288, No. 10, A539-A542 (1979).
W. T. F. Blakeley and A. J. Pritchard, “Stability of abstract evolution equations,” in: Contr. Distrib. Parameter Syst. Proc. 2nd IFAC Symp., Coventry, 1977, Oxford (1978), pp. 121–132.
O. Bratteli, A. Kishimoto, and D. W. Robinson, “Positivity and monotonity properties of C0-semigroups. I,” Commun. Math. Phys.,75, No. 1, 67–84 (1980).
D. Brezis, “Classes d'interpolation associées à un opérateur monotone,” C. R. Acad. Sci.,276, No. 24, A1553–1556 (1973).
H. Brezis, “Perturbations non linéaires d'opérateurs maximaux monotones,” C. R. Acad. Sci.,269, No. 14, A566-A569 (1969).
H. Brezis, “Properties régularisantes de certains semigroupes non linéaires,” Isr. J. Math.,9, No. 4, 513–534 (1971).
H. Brezis, “Semigroupes non linéaires et applications,” in: Symp. Math. Inst. Naz. Alta Mat., Vol. 7, London-New York (1971), pp. 3–27.
H. Brezis, “Un problème d'évolution avec contraintes unilatérales dépendant du temps,” C. R. Acad. Sci.,274, No. 4, A310-A312 (1972).
H. Brezis, “Problèmes unilatéraux,” J. Math. Pures Appl.,54, No. 1 (1972).
H. Brezis, “Inéquations variationnelles relatives à l'opérateur de Navier-Stokes,” J. Math. Anal. Appl.,39, No. 1, 159–165 (1972).
H. Brezis, Operateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert, North-Holland Math. Stud., North-Holland, Amsterdam-London-New York (1973).
H. Brezis, “Nonlinear perturbations of monotone operators,” Univ. Kansas Dep't. Math. Tech. Rept., No. 25 (1972).
H. Brezis, “Quelques proprietes des operateurs monotones et des semigroupes non linéaires,” Lect. Notes Math.,543, 56–82 (1976).
H. Brezis and F. E. Browder, “A general principle on ordered sets in nonlinear functional analysis,” Adv. Math.,21, No. 3, 355–364 (1976).
H. Brezis and F. E. Browder, “Nonlinear ergodic theorems,” Bull. AMS,82, No. 6, 959–961 (1976).
H. Brezis and F. E. Browder, “Remarks on nonlinear ergodic theory,” Adv. Math.,25, No. 2, 165–177 (1977).
H. Brezis, M. G. Crandall, and A. Pazy, “Perturbations of nonlinear maximal monotone sets in Banach space,” Commun. Pure Appl. Math.,23, No. 1, 123–144 (1970).
H. Brezis and A. Haraux, “Image d'une somme d'operateurs monotones et applications,” Isr. J. Math.,23, No. 2, 165–186 (1976).
H. Brezis and T. Kato, “Remarks on the Schrödinger operators with singular complex potentials,” J. Math. Pures Appl.,58, No. 2, 137–151 (1979).
H. Brezis and L. Nirenberg, “Image d'une somme d'opérateurs non linéaires et applications,” C. R. Acad. Sci.,284, No. 21, A1365-A1368 (1977).
H. Brezis and L. Nirenberg, “Characterization of the ranges of some nonlinear operators and applications to boundary value problems,” Ann. Scuola Norm. Super. Pisa, Cl. Sci.,5, No. 2, 225–326 (1978).
H. Brezis and A. Pazy, “Semigroups of nonlinear contractions on convex sets,” J. Funct. Anal.,6, No. 2, 237–281 (1970).
H. Brezis and A. Pazy, “Accretive sets and differential equations in Banach spaces,” Isr. J. Math.,8, No. 4, 367–383 (1970).
H. Brezis and A. Pazy, “Convergence and approximation of semigroups of nonlinear operators in Banach spaces,” J. Funct. Anal.,9, No. 1, 63–74 (1972).
R. E. Bruck, Jr., “Asymptotic convergence of nonlinear contraction semigroups in Hilbert space,” J. Funct. Anal.,18, No. 1, 15–26 (1975).
R. E. Bruck, Jr., “On the almost-convergence of iterates of a nonexpansive mapping in Hilbert space and the structure of the weak ω-limit set,” Isr. J. Math.,29, No. 1, 1–16 (1978).
B. C. Burch, “A semigroup treatment of the Hamilton-Jacobi equation in several space variables,” J. Diff. Equat.,23, No. 1, 107–124 (1977).
B. C. Burch and J. A. Goldstein, “Nonlinear semigroups and a problem in heat conduction,” Houston J. Math.,4, No. 3, 311–328 (1978).
G. Busoni and G. Frosali, “Streaming operators and semigroups,” Meccanica,14, No. 3, 119–128 (1979).
B. D. Calvert, “Nonlinear evolution equations in Banach lattices,” Bull. AMS,76, No. 4, 845–850 (1970).
B. D. Calvert, “Nonlinear equations of evolution,” Pac. J. Math.,39, No. 2, 293–350 (1971).
B. D. Calvert, “On T-accretive operators,” Ann. Mat. Pura Appl.,94, 291–314 (1972).
B. D. Calvert, “Perturbation by Nemytskii operators of m-T-accretive operators in Lq,qε(1, ∞),” Rev. Roum. Math. Pures Appl.,22, No. 7, 883–906 (1977).
B. D. Calvert, “Perturbation of nonlinear hypercontractive semigroups,” Tohoku Math. J.,29, No. 4, 463–471 (1977).
B. D. Calvert and C. Picard, “Opérateurs accrétifs et ϕ -accrétifs dans un espace de Banach,” Hiroshima Math. J.,8, No. 1, 11–30 (1978).
S. Campanato, “Regolarità-C0,α, e regolarità-LP per soluzioni del problema di Cauchy astratto senza l'ipotezi di simmetria,” Boll. Unione Mat. Ital.,14A, No. 2, 409–418 (1977).
S. Camapanato, “Generation of analytic semigroups by elliptic operators of second order in Hölder spaces,” Ann. Scu. Norm. Super. Pisa. Cl. Sci.,8, No. 3, 495–512 (1981).
F. Cardoso and J. Hounie, “Globally hypoanalytic first-order evolution equations,” An. Acad. Brasil. Cienc.,49, No. 4, 533–535 (1977).
J. Carr, Applications of Centre Manifold Theory, Applied Math. Sci., Vol. 35, Berlin (1981).
R. Carrol and R. E. Showalter, Singular and Degenerate Cauchy Problems, Academic Press, New York (1976).
J. T. Chambers, “Some remarks on the approximation of nonlinear semigroups,” Proc. Jpn. Acad.,46, No. 6, 518–523 (1970).
J. T. Chambers and S. Oharu, “Semigroups of local Lipschitzians in a Banach space,” Pac. J. Math.,39, No. 1, 89–112 (1971).
J. Chazarain, “Problèmes de Cauchy au sens des distributions vectorielles et applications,” C. R. Acad. Sci.,266, No. 1, A10-A13 (1968).
J. Chazarain, “Un résultat de perturbation pour les générateurs de semigroupes et applications,” C. R. Acad. Sci.,267, No. 1, A13-A15 (1968).
J. Chazarain, “Problèmes de Cauchy abstraits et applications à quelques problèmes mixtes,” J. Funct. Anal.,7, No. 3, 386–446 (1971).
P. R. Chernoff, “Note on product formulas for operator semigroups,” J. Funct. Anal.,2, No. 2, 238–242 (1968).
P. R. Chernoff, “Semigroup product formulas and addition of unbounded operators,” Bull. AMS,76, No. 2, 395–398 (1970).
P. R. Chernoff, “Perturbations of dissipative operators with relative bound one,” Proc. AMS,33, No. 1, 72–74 (1972).
P. R. Chernoff, “Product formulas, nonlinear semigroups, and addition of unbounded operators,” Mem. AMS, No. 140 (1974).
P. R. Chernoff, “A note on continuity of semigroups of maps,” Proc. AMS,53, No. 2, 318–320 (1975).
P. R. Chernoff, “On the converse of the Trotter product formula,” Ill. J. Math.,20, No. 2, 348–353 (1976).
P. R. Chernoff, “Two counterexamples in semigroup theory on Hilbert space,” Proc. AMS,56, 253–255 (1976).
P. R. Chernoff and J. E. Marsden, “On continuity and smoothness of group actions,” Bull. AMS,76, No. 5, 1044–1049 (1970).
P. R. Chernoff and J. E. Marsden, “Properties of infinite dimensional Hamiltonian systems,” Lect. Notes Math.,425 (1974).
I. Cioranescu, “La caractérisation spectrale d'opérateurs, générateurs des semigroupes distributions d'ordre fini de croissance,” J. Math. Anal. Appl.,34, No. 1, 34–41 (1971).
I. Cioranescu, “Sur les semigroups ultradistributions,” J. Math. Anal. Appl.,41, No. 3, 539–544 (1973).
II. Cioranescu, “Sur la somme des générateurs de certains semigroupes distributions continus,” Rend. Mat.,6, No. 4, 785–801 (1973).
I. Cioranescu, “On periodic distribution groups,” in: Top. Mod. Oper. Theory. 5 Int. Conf. Oper. Theory, Timisoara and Herculane, June 2–12, 1980, Basel (1981), pp. 53–69.
I. Cioranescu and L. Zsido, “Opérateursω-ultradifférentiels,” C. R. Acad. Sci.,AB285, No. 12, A753-A756 (1977).
I. Cioranescu and L. Zsido, “Analytic generators for one-parameter groups,” Tohoku Math. J.,28, No. 3, 327–363 (1976).
C. V. Coffman and C. L. Grover, “Obtuse cones in Hilbert spaces and application to partial differential equations,” J. Funct. Anal.,15, No. 3, 369–396 (1980).
A. Corduneanu, “A theorem on the perturbation of the m-dissipative mappings,” Bull. Inst. Politech. Iasi, Sec. 1,21, Nos. 1–2, 13–16 (1975).
M. G. Crandall, “The semigroup approach to first-quasilinear equations in several space variables,” Isr. J. Math.,12, No. 2, 108–132 (1972).
M. G. Crandall, “A generalized domain for semigroup generators,” Proc. AMS,37, No. 2, 434–440 (1973).
M. G. Crandall and L. C. Evans, “On the relation of the operator\(\frac{\partial }{{\partial s}} \oplus \frac{\partial }{{\partial \tau }}\) to evolution governed by accretive operators},” Isr. J. Math.,21, No. 4, 261–278 (1975).
M. G. Crandall and T. M. Liggett, “Generation of semigroups of nonlinear transformations on general Banach spaces,” Am. J. Math.,93, No. 2, 265–298 (1971).
M. G. Crandall and T. M. Liggett, “A theorem and a counterexample in the theory of semigroups of nonlinear transformations,” Trans. Am. Math. Soc.,160, 263–278 (1971).
M. G. Crandall and J. A. Nohel, “An abstract functional differential equation and a related nonlinear Volterra equation,” Isr. J. Math.,29, No. 4, 313–328 (1978).
M. G. Crandall and A. Pazy, “Semigroups of nonlinear contractions and dissipative sets,” J. Funct. Anal.,3, No. 3, 376–418 (1969).
M. G. Crandall and A. Pazy, “On the differentiability of weak solutions of a differential equation in Banach space,” J. Math. Mech.,18, No. 10, 1007–1016 (1969).
M. G. Crandall and A. Pazy, “Nonlinear evolution equations in Banach spaces,” Isr. J. Math.,11, No. 1, 57–94 (1972).
M. G. Crandall and A. Pazy, “On the range of accretive operators,” Isr. J. Math.,27, Nos. 3–4, 235–246 (1977).
M. G. Crandall and A. Pazy, “An approximation of integrable functions by step functions with an application,” Proc. AMS,76, No. 1, 74–80 (1979).
M. G. Crandall, A. Pazy, and L. Tartar, “Remarks on generators of analytic semigroups,” Isr. J. Math.,32, No. 4, 363–374 (1979).
M. G. Crandall and R. S. Phillips, “On the extension problems for dissipative operators,” J. Funct. Anal.,2, No. 2, 147–176 (1968).
M. G. Crandall and M. Pierre, “Regularizing effects foru t +Aϕ(u)=0 in L1,” J. Funct. Anal.,45, No. 2, 194–212 (1982).
M. G. Crandall and P. H. Rabinovitz, “The Hopf bifurcation theorem in infinite dimensions,” Arch. Ration. Mech. Anal.,67, No. 1, 53–72 (1977).
M. G. Crandall and P. H. Rabinovitz, “The principle of exchange of stability,” in: Dyn. Syst. Proc. Univ. Fla. Int. Symp., Gainesville, 1976, New York (1977), pp. 27–41.
M. G. Crandall and L. Tartar, “Some relations between nonexpansive and order preserving mappings,” Proc. AMS,78, No. 3, 385–390 (1980).
G. Da Prato, “Semigruppi di crescenza n,” Ann. Scuola Norm. Super. Pisa. Sci. Fis. Mat.,20, No. 4, 753–782 (1966).
G. Da Prato, “Semigruppi regolarizzabili,” Ricerche Mat.,15, No. 2, 223–248 (1966).
G. Da Prato, “Somma di generatori infinitesimali di semigruppi di contrazione e equazioni di evoluzione in spazi di Banach,” Ann. Mat. Pura Appl.,78, 131–157 (1968).
G. Da Prato, “Somma di generatori infinitesimali di semigruppi analitici,” Rend. Sem. Mat. Univ. Padova,40, 151–161 (1968).
G. Da Prato, “R-semigruppi analitici ed equazioni di evoluzione in LP,” Ricerche Mat.,16, No. 2, 233–249 (1967).
G. Da Prato, “Somma di generatori infinitesimali di semigruppi di contrazione e equazioni di evoluzione in spazi di Banach riflessivi,” Boll. Unione Mat. Ital.,1, No. 1, 138–141 (1968).
G. Da Prato, “Somme de générateur infinitésimaux de classe C0,” Atti. Acad. Naz. Lincei. Rend. Cl. Sci. Fis., Mat. Natur.,45, Nos. 1–2, 14–21 (1968).
G. Da Prato, “Équations d'évolution dans des algèbres d'opérateurs et application à des equations quasilineaires,” J. Math. Pures Appl.,48, No. 1, 59–107 (1969).
G. Da Prato, “Weak solutions for linear abstract differential equations in Banach spaces,” Adv. Math.,5, No. 2, 181–245 (1970).
G. Da Prato, “Somme d'applications non linéaires dans des cones et équations dans des espaces d'opérateurs,” J. Math. Pures Appl.,49, No. 4, 289–348 (1970).
G. Da Prato, “Somme d'applications nonlinéaires,” in: Symp. Mat. Ist. Naz. Alta Mat., Vol. 7, London-New York (1971), pp. 233–268.
G. Da Prato, “Quelques résultats d'existence et régularité pour un problème non linéaire de la théorie du contrôle,” Bull. Soc. Math. France, Mem. Nos. 31–32, 127–132 (1972).
G. Da Prato, “Quelques résultats d'existence, unicité et régulairite pour un problème de la théorie du contrôle,” J. Math. Pures Appl.,52, No. 4, 353–375 (1973 (1974)).
G. Da Prato, “Applications croissantes et équations d'évolution dans les espaces de Banach,” in: Inst. Math. Vol. 2. Corso lezioni Ist. Naz. Alta Mat. Febbr. Maggio, 1975, Academic Press, London-New York (1976 (1977)).
G. Da Prato and P. Grisvard, “Sommes d'opérateurs linéaires et équations différentielles opérationelles,” J. Math. Pures Appl.,54, No. 3, 305–387 (1975).
G. Da Prato and P. Grisvard, “Équations d'evolution abstraites non lineaires de type parabolique,” C. R. Acad. Sci.,283, No. 9, A709-A711 (1976).
G. Da Prato and P. Grisvard, “Équations d'évolution abstraites non lineaires de type parabolique,” Ann. Mat. Pura Appl.,120, 329–396 (1979).
G. Da Prato and U. Mosco, “Semigruppi distribuzione analitici,” Ann. Scuola Norm. Sup. Pisa. Sci. Fis. Mat.,19, No. 3, 367–396 (1965).
C. M. Dafermos, “Contraction semigroups and trend to equilibrium in continuum mechanics,” Lect. Notes Math.,503, 295–306 (1976).
C. M. Dafermos, “Almost-periodic processes and almost-periodic solutions of evolution equations,” in: Dyn. Syst. Proc. Univ. Fla. Int. Symp., Gainesville, 1976, New York (1977), pp. 43–57.
C. M. Dafermos, “Asymptotic behavior of solutions of evolution equations. Nonlinear evolution equations,” Proc. Symp. Math. Res. Center Univ. Wisc.-Madison, Oct. 17–19, 1977, Publ. Math. Res. Center Univ. Wisconsin-Madison, No. 40, Academic Press, New York (1978), pp. 103–123.
C. M. Dafermos and M. Slemrod, “Asymptotic behavior of nonlinear contraction semigroups,” J. Funct. Anal.,13, No. 1, 97–106 (1973).
A. Damlamian, “Resolution d'une équation differentielle hyperbolique non linéaire par une méthode d'evolution avec normes variables,” C. R. Acad. Sci.,277, No. 12, A525-A527 (1973).
R. Datko, “Uniform asymptotic stability of evolutionary processes in a Banach space,” SIAM J. Math. Anal.,3, No. 3, 428–445 (1972).
E. B. Davies, “Some contraction semigroups in quantum probability,” Z. Wahrscheinlichkeitstheor. Verw. Geb.,23, No. 4, 261–273 (1972).
E. B. Davies, “Markovian master equations,” Commun. Math. Phys.,39, No. 2, 91–110 (1974).
E. B. Davies, “Markovian master equations. II,” Math. Ann.,219, No. 2, 147–158 (1976).
E. B. Davies, “The classical limit for quantum dynamical semigroups,” Commun. Math. Phys.,49, No. 2, 113–129 (1976).
E. B. Davies, “Quantum dynamical semigroups and the neutron diffusion equation,” Repts. Math. Phys.,11, No. 2, 169–188 (1977).
E. B. Davies, “Asymptotic analysis of some abstract evolution equations,” J. Funct. Anal.,25, No. 1, 81–101 (1977).
E. B. Davies, “Generators of dynamical semigroups,” J. Funct. Anal.,34, No. 3, 421–431 (1979).
E. B. Davies, One-Parameter Semigroups, Academic Press, London (1980).
M. C. Delfour, “The largest class of hereditary systems defining a C0 semigroup on the product space,” Can. J. Math.,32, No. 4, 963–978 (1980).
R. Derndinger, “Über das Spektrum positiver Generatoren,” Math. Z.,172, No. 3, 281–293 (1980).
R. Derndinger and R. Nagel, “Generator stark stetiger Verbandshalbgruppen auf C(X) und dessen Spektrum,” Math. Ann.,245, No. 2, 159–177 (1979).
C. Devys and J.-M. Morel, “Stricte monotonie, stricte convexité et contractions strictes dans la théorie des semigroupes,” C. R. Acad. Sci., Ser. 1,292, No. 4, 267–270 (1981).
J. I. Diaz, “Anulacion de soluciones para operadores acretivos en espacios de Banach. Applicaciones e ciertos problemas parabolicos no lineales,” Rev. Acad. Cienc. Exact., Fis. Natur. Madrid,74, No. 5, 865–880 (1980).
J. A. Donaldson, “The Cauchy problem for a first-order system of abstract operator equations,” Bull. AMS,81, No. 3, Part 1, 576–578 (1975).
J. A. Donaldson, “The abstract Cauchy problem,” J. Diff. Equat.,25, No. 3, 400–409 (1977).
J. R. Dorroh, “A nonlinear Hille-Yosida-Phillips theorem,” J. Funct. Anal.,3, No. 3, 345–353 (1969).
J. R. Dorroh and R. A. Graff, “Integral equations in Banach spaces, a general approach to the linear Cauchy problem, and applications to the nonlinear problem,” J. Integr. Equat.,1, No. 4, 309–359 (1979).
J. R. Dorroh and T. F. Lin, “Markov processes with quasilinear first-order forward differential equations,” J. Math. Anal. Appl.,41, No. 1, 205–225 (1973).
J. R. Dorroh and T. F. Lin, “Markov processes with quasilinear parabolic forward differential equation,” Adv. Math.,19, No. 1, 19–47 (1976).
R.-M. Dubois, “Dissipativité locale des systèmes paraboliques pour différentes normes,” C. R. Acad. Sci., Ser. 1,294, No. 4, 155–158 (1982).
R.-M. Dubois, “Opérateurs locaux localement dissipatifs a valeurs dans un espace de Hilbert,” Lect. Notes Math.,906, 88–102 (1982).
L. C. Evans, “Nonlinear evolution equations in an arbitrary Banach space,” Isr. J. Math.,26, No. 1, 1–42 (1977).
L. C. Evans, “Differentiability of a nonlinear semigroup in L1,” J. Math. Anal. Appl.,60, No. 3, 703–715 (1977).
L. C. Evans, Applications of Nonlinear Semigroup Theory to Certain Partial Differential Equations. Nonlinear Evolution Equations. Publs. Math. Research Center, the Univ. of Wisconsin, Madison, No. 40, Academic Press, New York (1978).
W. G. Faris, “The product formula for semigroups defined by Friedrichs extensions,” Pac. J. Math.,22, No. 1, 47–70 (1967).
W. G. Faris, “Product formulas for perturbations of linear propagators,” J. Funct. Anal.,1, No. 1, 93–108 (1967).
H. O. Fattorini, “A representation theorem for distribution semigroups,” J. Funct. Anal.,6, No. 1, 83–96 (1970).
A. Favini, “Laplace transform method for a class of degenerate evolution problems,” Rend. Mat.,12, Nos. 3–4, 511–536 (1979).
A. Favini, “Some results on a class of degenerate evolution problems,” Atti. Acad. Naz. Lincei. Rend. Cl. Sci. Fis., Mat. Natur.,66, No. 1, 6–11 (1979).
W. Feller, “Semigroups of transformations in general weak topologies,” Ann. Math.,57, No. 2, 287–308 (1953).
W. E. Fitzgibbon, “Approximations of nonlinear evolution equations,” J. Math. Soc. Jpn.,25, No. 2, 211–221 (1979).
W. E. Fitzgibbon, “Nonlinear perturbations of m-accretive operators,” Proc. AMS,44, No. 2, 359–364 (1974).
G. Foias, “Remarque sur les semigroupes distributions d'opérateurs normaux,” Portug. Math.,19, Nos. 3–4, 227–242 (1960).
D. Fujiwara, “A characterisation of exponential distribution semigroups,” J. Math. Soc. Jpn.,18, No. 3, 267–274 (1966).
N. Fujiyama and J. Watanabe, “Convergence of subdifferentials and the penalty method,” Repts. Univ. Electro-Commun.,28, No. 2, 245–258 (1978).
L. Gearhart, “Spectral theory for contraction semigroups on Hilbert space,” Trans. AMS,236, 385–394 (1978).
J. S. Gibson, “A note on stabilization of infinite dimensional linear oscillators by compact linear feedback,” SIAM J. Control. Optim.,18, No. 3, 311–316 (1980).
Y. Giga, “The Stokes operator in Lr spaces,” Proc. Jpn. Acad.,A57, No. 2, 85–89 (1981).
Y. Giga, “Analyticity of the semigroup generated by the Stokes operator in Lr spaces,” Math. Z.,178, No. 3, 297–329 (1981).
J. A. Goldstein, “Some remarks on infinitesimal generators of analytic semigroups,” Proc. AMS,22, No. 1, 91–93 (1969).
J. A. Goldstein, “Lie product formula for one-parameter groups of isometries on Banach spaces,” Math. Ann.,186, No. 4, 299–306 (1970).
J. A. Goldstein, “Approximation of nonlinear semigroups and evolution equations,” J. Math. Soc. Jpn.,24, No. 4, 558–573 (1972).
J. A. Goldstein, “Semigroup theoretic proofs of the central limit theorem and other theorems of analysis,” Semigroup Forum,12, No. 3, 189–206 (1976).
J. A. Goldstein, “Some developments in semigroups since Hille-Phillips,” Integr. Equat. Oper. Theory,4, No. 3, 350–365 (1981).
H. Grabmüller, “Relativ akkretive Operatoren und Approximation von Evolutionsgleichungen 2. Art. I,” Math. Nachr.,66, 67–87 (1975).
H. Grabmüller, “Relativ akkretive Operatoren und Approximation von Evolutionsgleichungen 2. Art. II,” Math. Nachr.,66, 89–100 (1975).
G. Gripenberg, “On the asymptotic behavior of nonlinear contraction semigroups,” Math. Scand.,44, No. 2, 385–397 (1979).
P. Grisvard, “Equations differentielles abstraites,” Ann. Scient. Ecole Norm. Super.,2, No. 3, 311–395 (1969 (1970)).
K. Gröger and J. Nèčas. “On a class of nonlinear initial value problems in Hilbert spaces,” Math. Nachr.,93, 21–33 (1979).
M. Th. Guichet, “Reductible de certains équations différentielles dans des espaces de Banach de dimension quelconque,” Int. J. Non-Linear Mech.,13, Nos. 5–6, 273–284 (1978).
J.-P. Guillement and The Lai Pham, “Caractérisations des semigroupes distributions,” C. R. Acad. Sci.,A278, No. 18, 1173–1175 (1974).
J.-P. Guillement and The Lai Pham, “Sur la caractérisation des semigroupes distributions,” J. Fac. Sci. Univ. Tokyo, Sec. 1A,22, No. 3, 299–318 (1975).
H. Günzler and S. Zaidman, “Almost-periodic solutions of a certain abstract differential equation,” J. Math. Mech.,19, No. 2, 155–158 (1969).
K. Gustafson, “A perturbation lemma,” Bull. AMS,72, No. 2, 334–338 (1966).
K. Gustafson and G. Lumer, “Multiplicative perturbation of semigroup generators,” Pac. J. Math.,41, No. 3, 731–742 (1972).
K. Gustafson and K. Sato, “Some perturbation theorems for nonnegative contraction semigroups,” J. Math. Soc. Jpn.,21, No. 2, 200–204 (1969).
K. S. Ha, “Sur des semigroupes non linéaires dans les espaces L∞(Ω),” J. Math. Soc. Jpn.,31, No. 4, 593–622 (1979).
J. K. Hale, Topics in Dynamic Bifurcation Theory, Reg. Conf. Ser. Math., No. 47, Am. Math. Soc., Providence, R.I. (1981).
A. Haraux, “Équations d'évolution non linéaires: solutions bornées et périodiques,” Ann. Inst. Fourier,28, No. 2, 201–220 (1978).
A. Haraux, Nonlinear Evolution Equations — Global Behaviour of Solutions, Lect. Notes Math., Vol. 841 (1981).
S. Hasegawa, R. Sato, and S. Tsurumi, “Vector valued ergodic theorems for one-parameter semigroups of linear operators,” Tohoku Math. J.,30, No. 1, 95–106 (1978).
T. L. Hayden and P. J. Massey, III, “Nonlinear holomorphic semigroups,” Pac. J. Math.,57, No. 2, 423–439 (1975).
D. J. Hebert, “Probability methods and nonlinear analysis,” J. Funct. Anal.,17, No. 3, 239–262 (1974).
D. J. Hebert, “Nonlinear parabolic equations and probability,” Bull. AMS,80, No. 5, 965–969 (1974).
I. W. Herbst and A. D. Sloan, “Perturbation of translation invariant positivity preserving semigroups on L2(R N),” Trans. AMS,236, 325–360 (1978).
H. Hess, R. Schrader, and D. A. Uhlenbrock, “Domination of semigroups and generalization of Kato's inequality,” Duke Math. J.,44, No. 4, 893–904 (1977).
E. Hille, “On the differentiability of semigroup operators,” Acta Sci. Math. (Szeged),12B, 19–24 (1950).
N. Hirano, “Nonlinear ergodic theorems and weak convergence theorems,” J. Math. Soc. Jpn.,34, No. 1, 35–46 (1983).
N. Hirano and N. Takahashi, “Nonlinear ergodic theorems for nonexpansive mappings in Hilbert spaces,” Kodai Math. J.,2, No. 1, 11–25 (1979).
Ph. Holmes and J. Marsden, “A partial differential equation with infinitely many periodic orbits: chaotic oscillations of a forced beam,” Arch. Ration. Mech. Anal.,76, No. 2, 135–165 (1981).
M. Ianelli, “Nonlinear semigroups on cones of a nonreflexive Banach space,” Boll. Unione Mat. Ital.,2, No. 3, 412–419 (1970).
M. Ianelli, “A note on some nonlinear noncontraction semigroups,” Boll. Unione Mat. Ital.,3, No. 6, 1015–1025 (1970).
M. Ianelli, “Opérateurs dérivables et semigroupes non linéaires noncontractifs,” J. Math. Anal. Appl.,46, No. 3, 700–724 (1974).
T. Ichinose, “A product formula and its application to the Schrödinger equation,” Publs. Res. Inst. Math. Sci.,16, No. 2, 585–600 (1980).
M. M. Israel and S. Reich, “Asymptotic behavior of solutions of a nonlinear evolution equation,” J. Math. Anal. Appl.,83, No. 1, 43–53 (1981).
T. Itoh, “Hopf bifurcation of semilinear evolution equations,” Proc. Jpn. Acad.,A57, No. 4, 199–200 (1981).
T. Kato, “Note on a type of product formula for some nonlinear evolution equations,” Sci. Repts. Saitama Univ.,A9, No. 2, 1–9 (1979).
A. G. Kartsatos and J. Toro, “Passivity and admissibility for evolution equations in Banach spaces,” Nonlinear Anal.: Theory, Math. Appl.,6, No. 3, 225–236 (1982).
T. Kato, “A characterization of holomorphic semigroups,” Proc. AMS,25, No. 3, 495–498 (1970).
T. Kato, “Schrödinger operators with singular potentials,” Isr. J. Math.,13, Nos. 1–2, 135–148 (1972).
T. Kato, “On the Trotter-Lie product formula,” Proc. Jpn. Acad.,50, No. 9, 694–698 (1974).
T. Kato, “Singular perturbation and semigroup theory,” Lect. Notes Math.,565, 104–112 (1976).
T. Kato, “On some Schrödinger operators with a singular complex potential,” Ann. Scu. Norm. Super. Pisa, Cl. Sci.,5, No. 1, 105–114 (1978).
T. Kato and K. Masuda, “Trotter's product formula for nonlinear semigroups generated by the subdifferentials of convex functionals,” J. Math. Soc. Jpn.,30, No. 1, 169–178 (1978).
N. Kenmochi, “Remarks on the m-accretiveness of nonlinear operators,” Hiroshima Math. J.,3, No. 1, 61–68 (1973).
N. Kenmochi, “Some nonlinear parabolic variational inequalities,” Isr. J. Math.,22, Nos. 3–4, 304–331 (1975).
N. Kenmochi, “Nonlinear evolution equations with variable domains in Hilbert spaces,” Proc. Jpn. Acad.,A53, No. 5, 163–166 (1977).
N. Kenmochi, “Nonlinear parabolic variational inequalities with time-dependent constraints,” Proc. Jpn. Acad.,A53, No. 6, 186–189 (1977).
N. Kenmochi, “Free boundary problems for a class of nonlinear parabolic equations: An approach by the theory of subdifferential operators,” J. Math. Soc. Jpn.,34, No. 1, 1–13 (1982).
N. Kenmochi and S. Oharu, “Difference approximation of nonlinear evolution equations and semigroups of nonlinear operators,” Publs. Res. Inst. Math. Sci.,10, No. 1, 147–207 (1974).
N. Kenmochi and T. Takahashi, “On the global existence of solutions of differential equations on closed subsets of a Banach space,” Proc. Jpn. Acad.,51, No. 7, 520–525 (1975).
R. P. Kertz, “Limit theorems for semigroups with perturbed generators with applications to multiscaled random evolutions,” J. Funct. Anal.,27, No. 2, 215–233 (1978).
R. P. Kertz, “A semigroup perturbation theorem with application to a singular perturbation problem in nonlinear ordinary differential equations,” J. Diff. Equat.,31, No. 1, 1–15 (1979).
W. A. Kirk and R. Torrejon, “Asymptotically nonexpansive semigroups in Banach spaces,” Nonlinear Anal.: Theory, Meth. Appl.,3, No. 1, 111–121 (1979).
A. Kishimoto and D. W. Robinson, “Positivity and monotonicity properties of C0-semigroups. II,” Commun. Math. Phys.,75, No. 1, 85–101 (1980).
J. Kisynsky, “Semigroups of operators and some of their applications to partial differential equations,” in: Contr. Theory and Top. Funct. Anal., Vol. 3, Vienna (1976), pp. 305–405.
A. Klein and L. S. Landau, “Singular perturbations of positivity preserving semigroups via path space techniques,” J. Funct. Anal.,20, No. 1, 44–82 (1975).
I. Kluvanek, “Representations integrals d'evolutions perturbees,” C. R. Acad. Sci.,AB288, No. 23, A1065-A1067 (1979).
Y. Kobayashi, “On approximation of nonlinear semigroups,” Proc. Jpn. Acad.,50, No. 9, 729–734 (1974).
Y. Kobayashi, “Difference approximation of evolution equations and generation of non-linear semigroups,” Proc. Jpn. Acad.,51, No. 6, 406–410 (1975).
Y. Kobayashi, “Difference approximation of Cauchy problems for quasidissipative operators and generation of nonlinear semigroups,” J. Math. Soc. Jpn.,27, No. 4, 640–665 (1975).
Y. Kobayashi and K. Kobayasi, “On perturbation of nonlinear equations in Banach spaces,” Publs. Res. Inst. Math. Sci.,12, No. 3, 709–725 (1977).
K. Kobayasi, “Note on approximation of nonlinear semigroups,” Proc. Jpn. Acad.,50, No. 9, 735–737 (1974).
K. Kobayasi, “On a theorem for linear evolution equations of hyperbolic type,” J. Math. Soc. Jpn.,31, No. 4, 647–654 (1979).
K. Kobayasi and I. Miyadera, “On the strong convergence of the Cesaro means of contractions in Banach spaces,” Proc. Jpn. Acad.,A56, No. 6, 245–249 (1980).
Y. Koi and J. Watanabe, “On nonlinear evolution equations with a difference term of subdifferentials,” Proc. Jpn. Acad.,57, No. 1, 413–416 (1976).
T. Komura, “Semigroups of operators in locally convex spaces,” J. Funct. Anal.,2, No. 2, 258–296 (1968).
Y. Komura, “Differentiability of nonlinear semigroups,” J. Math. Soc. Jpn.,21, No. 3, 375–402 (1969).
Y. Komura, “On linear evolution operators in reflexive Banach spaces,” J. Fac. Sci. Univ. Tokyo, Sec. 1A,17, No. 3, 529–542 (1970).
Y. Konishi, “Nonlinear semigroups in Banach lattices,” Proc. Jpn. Acad.,47, No. 1, 24–28 (1971).
Y. Konishi, “A remark on perturbation of m-accretive operators in Banach space,” Proc. Jpn. Acad.,47, No. 5, 452–455 (1971).
Y. Konishi, “Some examples of nonlinear semigroups in Banach lattices,” J. Fac. Sci. Univ. Tokyo, Sec. 1A,18, No. 3, 537–543 (1972).
Y. Konishi, “On the uniform convergence of a finite difference scheme for a nonlinear heat equation,” Proc. Jpn. Acad.,48, No. 2, 62–66 (1972).
Y. Konishi, “Sur la compacité des semigroupes non linéaires dans les espaces de Hilbert,” Proc. Jpn. Acad.,48, No. 5, 278–280 (1972).
Y. Konishi, “Une remarque sur la perturbation d'opérateurs m-accrétifs dans un espace de Banach,” Proc. Jpn. Acad.,48, No. 3, 157–160 (1972).
Y. Konishi, “Une méthode de résolution d'une équation d'évolution non linéaire dégéneree,” J. Fac. Sci. Univ. Tokyo, Sec. 1A,19, No. 2, 243–255 (1972).
Y. Konishi, “On ut = uxx − F(ux) and the differentiability of the nonlinear semigroup associated with it,” Proc. Jpn. Acad.,48, No. 5, 281–286 (1972).
Y. Konishi, “Sur un système dégéneré des équations paraboliques semilinéaires avec les conditions aux limites non linéaires,” J. Fac. Sci. Univ. Tokyo, Sec. 1A,19, No. 3, 353–361 (1972).
Y. Konishi, “A remark on semigroups of local Lipschitzians in Banach space,” Proc. Jpn. Acad.,47, No. 2, 970–973 (1971).
Y. Konishi, “A remark on fluid flows through porous media,” Proc. Jpn. Acad.,49, No. 1, 20–24 (1973).
Y. Konishi, “On the nonlinear semigroups associated with ut = Δ β(u) and ϕ (ut) = Δu,” J. Math. Soc. Jpn.,25, No. 4, 622–628 (1973).
Y. Konishi, “Une remarque sur des problèmes de perturbations singulières et d'évolution,” C. R. Acad. Sci.,282, No. 15, A775-A777 (1976).
T. Koyama and T. Ichinose “On the Trotter product formula,” Proc. Jpn. Acad.,A57, No. 2, 95–100 (1981).
U. Krengel, “Recent progress on ergodic theorems,” Asterisque, No. 50, 151–192 (1977).
T. G. Kurtz, “Convergence of operator semigroups with applications to Markov processes,” Doct. Diss., Stanford University (1967).
T. G. Kurtz, “Extensions of Trotter's operator semigroup approximation theorems,” J. Funct. Anal.,3, No. 3, 354–375 (1969).
T. G. Kurtz, “A general theorem on the convergence of operator semigroups,” Trans. AMS,148, No. 1, 23–32 (1970).
T. G. Kurtz, “Approximation of age dependent, multitype branching processes,” Ann. Stat.,41, No. 2, 363–368 (1970).
T. G. Kurtz, “Convergence of sequences of semigroups of nonlinear operators with an application to gas kinetics,” Trans. AMS,186, Dec., 259–272 (1973).
T. G. Kurtz, “A random Trotter product formula,” Proc. AMS,35, No. 1, 147–154 (1972).
T. G. Kurtz, “A limit theorem for perturbed operator semigroups with applications to random evolutions,” J. Funct. Anal.,12, No. 1, 55–67 (1973).
T. G. Kurtz, “A variational formula for the growth rate of a positive operator semigroup,” SIAM J. Math. Anal.,10, No. 1, 112–117 (1979).
J. E. Lagnese, “Singular differential equations in Hilbert space,” SIAM J. Math. Anal.,4, No. 4, 623–637 (1973).
J. E. Lagnese, “On equations of evolution and parabolic equations of higher order in t,” J. Math. Anal. Appl.,32, No. 1, 15–37 (1970).
M. Lapidus, “Formules de moyenne et de produit pour les résolvantes imaginaires d'opérateurs autoadjoints,” C. R. Acad. Sci.,AB291, No. 7, A451-A454 (1980).
M. Lapidus, “Perturbation d'un semigroupe par un groupe unitaire,” C. R. Acad. Sci.,AB291, No. 9, A535-A538 (1980).
M. Lapidus, “Généralisation de la formule de Trotter-Lie,” C. R. Acad. Sci.,AB291, No. 8, A497-A500 (1980).
M. Lapidus, “Generalization of the Trotter-Lie formula,” Integr. Equat. Oper. Theory,4, No. 3, 366–415 (1981).
E. Larsson, “Generalized distribution semigroups of bounded linear operators,” Ann. Scuola Norm. Super. Pisa. Sci. Fis. Mat.,21, No. 2, 137–159 (1967).
I. Lasiecka, “Unified approach for abstract parabolic boundary problems — a semigroup approach,” Appl. Math. Optim.,6, No. 4, 287–333 (1980).
N. Levan, “On the unitary subspace of a dissipative perturbation of a contraction semigroup,” Indiana U. Math. J.,28, No. 2, 241–249 (1979).
N. Levan and L. Rigby, “On the reduction of a contraction semigroup to a completely nonunitary semigroup,” J. Math. Anal. Appl.,67, No. 1, 1–11 (1979).
C. H. Lê, “Dérivability d'un semigroupe engendré par un operateur m-accretif de L1(Ω) et accretif dans L∞(Ω),” C. R. Acad. Sci.,283, No. 7, A469-A472 (1976).
T. M. Liggett, “Existence theorems for infinite particle systems,” Trans. AMS,165, March, 471–481 (1972).
G. Lindblad, “On the generators of quantum dynamical semigroups,” Commun. Math. Phys.,48, No. 2, 119–130 (1976).
J. L. Lions, “Some aspects of the theory of linear evolution equations,” in: Boundary Value Problems. Linear Evolution. Partial Differential Equations. Proc. NATO Adv. Study Inst., Liege, 1976. Dordrecht-Boston (1977), pp. 175–238.
J. L. Lions, “Les semigroupes distributions,” Portug. Math.,19, Nos. 3–4, 141–161 (1960).
P. L. Lions and B. Mercier, “Splitting algorithms for the sum of two nonlinear operators,” SIAM J. Numer. Anal.,16, No. 6, 964–979 (1979).
D. L. Lovelady, “Semigroups of linear operators on locally convex spaces with Banach subspaces,” Indiana Univ. Math. J.,24, No. 12, 1197–1198 (1975).
D. L. Lovelady, “Un criterio per la continuité de-l'addizione di Lie-Chernoff,” Ann. Univ. Ferrara, Sez. VII,20, 65–68 (1975).
V. Lovicar, “Periodic solutions of nonlinear abstract second-order equations with dissipative terms,” Cas. Pestov. Mat.,102, No. 4, 364–369 (1977).
G. Lumer, “Perturbation de générateurs infinitésimaux du type ‘changement de temps’,” Ann. Inst. Fourier,23, No. 4, 271–279 (1973(1974)).
G. Lumer, “Problème de Cauchy pour opérateurs locaux,” C. R. Acad. Sci.,281, No. 18, A763-A765 (1975).
G. Lumer, “Problème de Cauchy pour opérateurs locaux et ‘changement de temps’,” Ann. Inst. Fourier,25, Nos. 3–4, 409–446 (1975(1976)).
G. Lumer, “Problème de Cauchy avec valeurs au bord continues,” C. R. Acad. Sci.,281, No. 19, A805-A807 (1975).
G. Lumer, “Problème de Cauchy avec valeurs au bord continues, comportement asymptotique, et applications,” Lect. Notes Math.,563, 193–201 (1976).
G. Lumer, “Problème de Cauchy et fonctions superharmoniques,” Lect. Notes Math.,563, 202–218 (1976).
G. Lumer, “Équations d'évolution pour opérateurs locaux non localement fermés,” C. R. Acad. Sci.,284, No. 21, A1361-A1363 (1977).
G. Lumer, “Equations dévolution en norme uniforme pour opérateurs elliptiques. Régularité des solutions,” C. R. Acad. Sci.,284, No. 22, A1435-A1437 (1977).
G. Lumer, “Principe du maximum et équations d'évolution dans L2,” Lect. Notes Math.,681, 143–156 (1978).
G. Lumer, “Perturbations additives d'opérateurs locaux,” C. R. Acad. Sci.,AB288, No. 2, A107-A110 (1979).
G. Lumer, “Approximation des solutions d'équations d'évolution pour opérateurs locaux en général et pour opérateurs elliptiques,” C. R. Acad. Sci.,AB288, No. 3, A189-A192 (1979)
G. Lumer, “Connecting of local operators and evolution equations on networks,” Lect. Notes Math.,787, 219–234 (1980).
G. Lumer and L. Paquet, “Semigroupes holomorphes et équations d'évolution,” C. R. Acad. Sci.,284, No. 4, A237-A240 (1977).
G. Lumer and L. Paquet, “Semigroupes holomorphes, produit tensoriel de semigroupes et équations d'évolution,” Lect. Notes Math.,713, 156–177 (1979).
G. Lumer and R. S. Phillips, “Dissipative operators in a Banach space,” Pac. J. Math.,11, No. 2, 679–698 (1961).
M. A. Malik, “Regularity of elementary solutions of abstract differential equations,” Boll. Unione Mat. Ital.,4, No. 1, 78–84 (1971).
I. Marek, “Fundamental decay mode and asymptotic behavior of positive semigroups,” Czech. Math. J.,30, 579–589 (1980).
J. E. Marsden, “On product formulas for nonlinear semigroups,” J. Funct. Anal.,13, No. 1, 51–72 (1973).
J. E. Marsden, “The Hopf bifurcation for nonlinear semigroups,” Bull. AMS,79, No. 3, 537–541 (1973).
R. H. Martin, Jr., “A global existence theorem for autonomous differential equations in a Banach space,” Proc. AMS,26, No. 2, 307–314 (1970).
R. H. Martin, Jr., “Generating an evolution system in a class of uniformly convex Banach spaces,” J. Funct. Anal.,11, No. 1, 62–76 (1972).
R. H. Martin, Jr., “Differential equations on closed subsets of a Banach space,” Trans. AMS,179, May, 399–414 (1973).
R. H. Martin, Jr., Nonlinear Operators and Differential Equations in Banach Spaces, Wiley, New York (1976).
R. H. Martin, Jr., “Invariant sets for evolution systems,” Int. Conf. Diff. Equat., 1974, New York (1975), pp. 510–536.
K. Maruo, “On some evolution equations of subdifferential operators,” Proc. Jpn. Acad.,51, No. 5, 304–307 (1975).
K. Maruo and S. Yotsutani, “A certain degenerate evolution equation of the subdifferential type,” Osaka J. Math.,13, No. 2, 599–612 (1976).
T. Matahashi and M. Tsutsumi, “On a periodic problem for pseudoparabolic equations of Sobolev-Galperin type,” Math. Jpn.,22, No. 5, 535–553 (1978).
T. Matahashi and M. Tsutsumi, “Periodic solutions of semilinear pseudoparabolic equations in Hilbert space,” Funkc. Ekvacioj,22, No. 1, 51–66 (1979).
M. Megan and P. Preda, “On exponential dichotomy in Banach spaces,” Bull. Austral. Math. Soc.,23, No. 2, 293–306 (1981).
J. Mika, “Hilbert asymptotic expansion method for evolution equations in Banach spaces,” Nukleonika,23, No. 3, 221–236 (1978).
J. Mika, “Asymptotic method for singularly perturbed linear differential equations in Banach spaces,” Lect. Notes Math.,703, 263–270 (1979).
I. Miyadera, “On the convergence of nonlinear semigroups,” Tohoku Math. J.,21, No. 2, 221–236 (1969).
I. Miyadera, “On the convergence of nonlinear semigroups. II,” J. Math. Soc. Jpn.,21, No. 3, 403–412 (1969).
I. Miyadera, “Some remarks on semigroups of nonlinear operators,” Tohoku Math. J.,23, No. 2, 245–258 (1971).
I. Miyadera, “Generation of semigroups of nonlinear contractions,” J. Math. Soc. Jpn.,26, No. 3, 389–404 (1974).
I. Miyadera, “On the generation of semigroups of operators,” Tohoku Math. J.,24, No. 2, 251–261 (1972).
I. Miyadera, “On the infinitesimal generators and the asymptotic behavior of nonlinear contraction semigroups,” Proc. Jpn. Acad.,A58, No. 1, 1–4 (1982).
I. Miyadera, “Asymptotic behavior of almost-orbits of nonlinear contraction semigroups in Banach spaces,” in: Differential Equations and Their Applications. Proceedings of the Second Conference, Russe, June 29–July 4, 1981 [in Russian], Part 2, Russe (1982), pp. 500–508.
I. Miyadera and S. Oharu, “Approximation of semigroups of nonlinear operators,” Tohoku Math. J.,22, No. 1, 24–47 (1970).
I. Miyadera, S. Oharu, and N. Okazawa, “Generation theorems of semigroups of linear operators,” Publs. Res. Inst. Math. Sci.,8, No. 3, 509–555 (1973).
J.-J. Moreau, “Probleme d'evolution associe a un convexe mobile d'un espace hilbertien,” C. R. Acad. Sci.,276, No. 11, A791-A794 (1973).
J.-J. Moreau, “Evolution problem associated with a moving convex set in a Hilbert space,” J. Diff. Equat.,26, No. 3, 347–374 (1977).
J.-J. Moreau, “Approximation en graphe d'une évolution discontinue,” RAIRO Anal. Numer.,12, No. 1, 75–84 (1978).
P. de Mottoni and A. Schiaffino, “Bifurcation of periodic solutions of periodic evolution equations in a cone,” J. Diff. Equat.,45, No. 3, 408–430 (1982).
B. Nagy, “Spectral mappings theorems for semigroups of operators,” Acta Sci. Math.,38, Nos. 3–4, 343–351 (1976).
M. Nakao, “On the existence of bounded solutions for nonlinear evolution equations of parabolic type,” Math. Repts. Coll. Gen. Educ. Kyushu Univ.,11, No. 1, 1–14 (1977).
J. Naumann, “On a class of first-order evolution inequalities arising in heat conduction with memory,” SIAM J. Math. Anal.,10, No. 6, 1144–1160 (1979).
J. Naumann, “On evolution inequalities of Navier-Stokes type in three dimensions,” Ann. Mat. Pura Appl.,124, 107–125 (1980).
J. Naumann and M. Wulst, “On evolution inequalities of Bingham type in three dimensions. I,” J. Math. Anal. Appl.,68, No. 1, 211–227 (1979).
E. Nelson, “The free Markoff field,” J. Funct. Anal.,12, No. 2, 211–227 (1973).
J. W. Neuberger, “Product integral formula for nonlinear expansive semigroups and non-expansive evolution systems,” J. Math. Mech.,19, No. 5, 403–409 (1969).
J. W. Neuberger, “Analyticity and quasianalyticity for one-parameter semigroups,” Proc. AMS,25, No. 3, 488–494 (1970).
J. W. Neuberger, “Quasianalyticity and semigroups of bounded linear transformations,” Bull. AMS,78, No. 1, 85–87 (1972).
J. W. Neuberger, “Quasianalyticity and semigroups,” Bull. AMS,78, No. 6, 909–922 (1972).
J. W. Neuberger, “Quasianalytic semigroups of bounded linear transformations,” J. London Math. Soc.,7, No. 2, 259–264 (1973).
O. Nevanlinna and S. Reich, “Strong convergence of contraction semigroups and of iterative methods for accretive operators in Banach spaces,” Isr. J. Math.,32, No. 1, 44–58 (1979).
T. Nishida, “A note on a theorem of Nirenberg,” J. Diff. Geom.,12, No. 4, 629–633 (1977).
R. E. O'Brien, Jr., “Contraction semigroups, stabilization and the mean ergodic theorem,” Proc. AMS,71, No. 1, 89–94 (1978).
S. Oharu, “A note on the generation of nonlinear semigroups in a locally convex space,” Jpn. Acad.,43, No. 9, 847–851 (1967).
S. Oharu, “On the generation of semigroups of nonlinear contractions,” J. Math. Soc. Jpn.,22, No. 4, 526–550 (1970).
S. Oharu, “Semigroups of linear operators in a Banach space,” Publs. Res. Inst. Math. Sci.,7, No. 2, 205–260 (1971).
S. Oharu, “Eine Bemerkung zur Charakterisierung der Distributionhalbgruppen,” Math. Ann.,204, No. 3, 189–198 (1973).
S. Oharu and H. Sunouchi, “On the convergence of semigroups of linear operators,” J. Funct. Anal.,6, No. 2, 292–304 (1970).
S. Oharu and T. Takahashi, “A convergence theorem of nonlinear semigroups and its application to first-order quasilinear equations,” J. Math. Soc. Jpn.,26, No. 1, 124–160 (1974).
N. Okazawa, “Two perturbation theorems for contraction semigroups in a Hilbert space,” Proc. Jpn. Acad.,45, No. 10, 850–853 (1969).
N. Okazawa, “A perturbation theorem for linear contraction semigroups on reflexive Banach spaces,” Proc. Jpn. Acad.,47, Suppl. No. 2, 947–949 (1971).
N. Okazawa, “Perturbation of linear m-accretive operators,” Proc. AMS,37, No. 1, 169–174 (1973).
N. Okazawa, “A generation theorem for semigroups of growth order α,” Tohoku Math. J.,26, No. 1, 39–51 (1974).
N. Okazawa, “Operator semigroups of class (Dn),” Math. Jpn.,18, No. 1, 33–51 (1973).
N. Okazawa, “Singular perturbations of m-accretive operators,” J. Math. Soc. Jpn.,32, No. 1, 19–44 (1980).
H. Okochi, “A note on asymptotic strong convergence of nonlinear contraction semigroups,” Proc. Jpn. Acad.,A56, No. 3, 83–84 (1980).
H. Okochi, “Asymptotic strong convergence of nonlinear contraction semigroups,” Tokyo J. Math.,5, No. 1, 171–182 (1982).
M. Otani, “On existence of strong solutions for du/dt + ∂ψ1(u(t)) — ∂ψ2(u(t)) Э f(t),” J. Fac. Sci. Univ. Tokyo, Sec. 1A,24, No. 3, 575–605 (1977).
M. Otani and Y. Yamada, “On the Navier-Stokes equations in noncylindrical domains: An approach by the subdifferential operator theory,” J. Fac. Sci. Univ. Tokyo, Sec. 1A,25, No. 2, 185–204 (1978).
K. L. Ou Young, “Periodic solutions of conservation laws,” J. Math. Anal. Appl.,75, No. 1, 180–202 (1980).
L. V. Ovsjannikov, “Cauchy problem in a scale of Banach spaces and its application to shallow water theory justification,” Lect. Notes Math.,503, 426–437 (1976).
L. Paquet, “Semigroupes holomorphes en norme uniforme,” C. R. Acad. Sci.,AB286, No. 3, A161-A164 (1978).
L. Paquet, “Équations d'évolution pour opérateurs locaux et équations aux dérivés partielles,” C. R. Acad. Sci.,AB286, No. 4, A215-A218 (1978).
L. Paquet, “Opérateurs locaux dépendent du temps et problème de Cauchy,” C. R. Acad. Sci.,AB286, No. 14, A613-A616 (1978).
L. Paquet, “Semigroupes holomorphes en norme du sup,” Lect. Notes Math.,713, 194–242 (1979).
G. B. Passty, “Preservation of the asymptotic behavior of a nonlinear contraction semigroup by backward differencing,” Houston J. Math.,7, No. 1, 103–110 (1981).
N. H. Pavel, “Nonlinear evolution equations governed by F-quasidissipative operators,” Nonlinear Anal.: Theory, Meth., Appl.,5, No. 5, 449–468 (1981).
N. H. Pavel, “Addendum-nonlinear evolution equations governed by F-quasidissipative operators,” Nonlinear Anal.: Theory, Meth., Appl.,5, No. 12, 1389 (1981).
A. Pazy, “On the differentiability and compactness of semigroups of linear operators,” J. Math. Mech.,17, No. 12, 1131–1141 (1968).
A. Pazy, “Asymptotic behavior of the solution of an abstract equation and some applications,” J. Diff. Equat.,4, No. 4, 493–509 (1968).
A. Pazy, “Approximation of the identity operator by semigroups of linear operators,” Proc. AMS,30, No. 1, 147–150 (1971).
A. Pazy, “Trotter-Lie formula for compactly generated semigroups of nonlinear operators,” J. Funct. Anal.,23, No. 4, 353–361 (1976).
A. Pazy, “On the asymptotic behavior of semigroups of nonlinear contractions in Hilbert space,” J. Funct. Anal.,27, No. 3, 292–307 (1978).
A. Pazy, “The asymptotic behavior of semigroups of nonlinear contractions having large sets of fixed points,” Proc. R. Soc. Edinburgh,A80, Nos. 3–4, 261–271 (1978).
A. Pazy, “Strong convergence of semigroups of nonlinear contractions in Hilbert space,” J. Anal. Math.,34, 1–35 (1978).
A. Pazy, “Remarks on nonlinear ergodic theory in Hilbert space,” Nonlinear Anal.: Theory, Meth. Appl.,3, No. 6, 863–871 (1979).
A. Pazy, “Semigroups of nonlinear contractions and their asymptotic behavior,” Res. Notes Math., No. 30, 36–134 (1979).
A. Pazy, “The Lyapunov method for semigroups of nonlinear contractions in Banach spaces,” J. Anal. Math.,40, 239–262 (1981).
J.-C. Peralba, “Un probleme d'evolution relatif a un operateur sous-differential dependent du temps,” C. R. Acad. Sci.,275, No. 2, A93-A96 (1972).
R. S. Phillips, “Perturbation theory for semigroups of linear operators,” Trans. AMS,74, No. 2, 199–221 (1953).
R. S. Phillips, “A note on the abstract Cauchy problem,” Proc. Nat. Acad. Sci. USA,40, No. 4, 244–248 (1954).
C. Picard, “Opérateurs ϕ-accrétifs et génération de semigroupes non linéaires,” C. R. Acad. Sci.,275, No. 14, A639-A641 (1972).
M. Pierre, “Un théorème général de génération de semigroups non linéaires,” Isr. J. Math.,23, Nos. 3–4, 189–199 (1976).
M. Pierre, “Perturbations localement Lipschitziennes et continues d'operateurs m-accretifs,” Proc. AMS,58, No. 1, 124–128 (1976).
M. Pierre, “Enveloppe d'une famille de semigroupes dans un espace de Banach,” C. R. Acad. Sci.,284, No. 7, A401-A404 (1977).
M. Pierre, “Invariant closed subsets for nonlinear semigroups,” Nonlinear Anal.: Theory, Meth., Appl.,2, No. 1, 107–117 (1978).
M. Pierre, “Équations d'évolution non linéaires, inéquations variationnelles et potentiels paraboliques,” These Doct. Etat. Sci. Math. Univ. Pierre et Marie Curie, Paris (1979).
G. H. Pimley, Jr. and B. Nikolaenko, “Some conditions for weak convergence to equilibrium of nonlinear contraction semigroups,” J. Diff. Equat.,29, No. 2, 269–277 (1978).
A. T. Plant, “Hölder continuous nonlinear product integrals,” Lect. Notes Math.,415, 417–421 (1974).
A. T. Plant, “Flow-invariant domains of Hölder continuity for nonlinear semigroups,” Proc. AMS,53, No. 1, 83–87 (1975).
A. T. Plant, “Some aspects of nonlinear semigroups,” in: Contr. Theory and Top. Funct. Anal., Vol. 3, Vienna (1976), pp. 291–304.
A. T. Plant, “The differentiability of nonlinear semigroups in uniformly convex spaces,” Isr. J. Math.,38, No. 3, 257–268 (1981).
N. N. Popescu and P. Preda, “Necessary and sufficient conditions for exponential dichotomies in Banach spaces,” An. Univ. Timisoara. Ser. Sti. Fiz.-Chim.,18, No. 2, 131–152 (1980).
P. Preda and M. Megan, “Admissibility and dichotomy for C0-semigroups,” An. Univ. Timisoara. Ser. Sti. Fiz.-Chim.,18, No. 2, 153–168 (1980).
S. Reich, “Asymptotic behavior of semigroups of nonlinear contractions in Hilbert spaces,” Atti Acad. Naz. Lincei. Rend. Cl. Sci. Fis., Mat. Natur.,56, No. 6, 866–872 (1974).
S. Reich, “Asymptotic behavior of semigroups of nonlinear contractions in Banach spaces,” J. Math. Anal. Appl.,53, No. 2, 277–290 (1976).
S. Reich, “Extension problems for accretive sets in Banach spaces,” J. Funct. Anal.,26, No. 4, 378–395 (1977).
S. Reich, “Product formulas, nonlinear semigroups, and accretive operators,” J. Funct. Anal.,36, No. 2, 147–168 (1980).
S. Reich, “Convergence and approximation of nonlinear semigroups,” J. Math. Anal. Appl.,76, No. 1, 77–83 (1980).
S. Reich, “On the asymptotic behavior of nonlinear semigroups and the range of accretive operators,” J. Math. Anal. Appl.,79, No. 1, 113–126 (1981).
S. Reich, “On the asymptotic behavior of nonlinear semigroups and the range of accretive operators. II,” J. Math. Anal. Appl.,87, No. 1, 134–146 (1982).
S. Reich, “A complement to Trotter's product formula for nonlinear semigroups generated by the subdifferentials of convex functionals,” Proc. Jpn. Acad.,A58, No. 5, 193–195 (1982).
S. Reich, “A nonlinear Hille-Yosida theorem in Banach spaces,” J. Math. Anal. Appl.,84, No. 1, 1–5 (1981).
S. Reich, “A characterization of nonlinear φ-accretive operators,” Manuscr. Math.,36, No. 2, 163–178 (1981).
H. M. Riedl and G. F. Webb, “Relative boundedness condition and the perturbation of non-linear operators,” Czech. Math. J.,24, No. 4, 584–597 (1974).
H. Röh, “Dissipative operators with finite dimensional damping,” Proc. R. Soc. Edinburgh,A91, Nos. 3–4, 243–263 (1982).
W. Rundell, “Determination of an unknown nonhomogeneous term in a linear partial differential equation from the overspecified boundary data,” Appl. Analysis,10, No. 3, 231–242 (1980).
M. Sable-Tougeron, “Problème d'évolution parabolique pour une classe d'opérateurs elliptiques et dégénerés,” Ann. Scu. Norm. Super. Pisa. Cl. Sci.,8, No. 3, 441–472 (1981).
N. Sanekata, “A note on the abstract Cauchy problem in a Banach space,” Proc. Jpn. Acad.,49, No. 7, 510–513 (1973).
N. Sanekata, “Some remarks on the abstract Cauchy problem,” Publs. Res. Inst. Math. Sci.,11, No. 1, 51–65 (1975).
K.-I. Sato, “On the generators of nonnegative contraction semigroups in Banach lattices,” J. Math. Soc. Jpn.,20, No. 3, 423–436 (1968).
K.-I. Sato, “On dispersive operators in Banach lattices,” Pac. J. Math.,33, No. 2, 429–443 (1970).
K.-I. Sato, “A note on nonlinear dispersive operators,” J. Fac. Sci. Univ. Tokyo, Sec. 1A,18, No. 3, 465–473 (1972).
K.-I. Sato, “A note on infinitesimal generators and potential operators of contraction semigroups,” Proc. Jpn. Acad.,48, No. 7, 450–453 (1972).
R. Sato, “Local ergodic properties of Lp-operator semigroups,” Comment. Math. Univ. Carol.,14, No. 1, 177–181 (1973).
R. Sato, “An Abel-maximal ergodic theorem for semigroups,” Pac. J. Math.,51, No. 2, 543–547 (1974).
R. Sato, “A note on a local ergodic theorem,” Comment. Math. Univ. Carol.,16, No. 1, 1–11 (1975).
R. Sato, “A mean ergodic theorem for a contraction semigroup in Lebesgue space,” Stud. Math. (PRL),54, No. 3, 213–219 (1976).
R. Sato, “Ergodic theorems for semigroups of positive operators,” J. Math. Soc. Jpn.,29, No. 4, 591–606 (1977).
R. Sato, “Contraction semigroups in Lebesgue space,” Pac. J. Math.,78, No. 1, 251–259 (1978).
N. Sauer, “Linear evolution equations in two Banach spaces,” Proc. R. Soc. Edinburgh,A91, Nos. 3–4, 287–303 (1982).
E. Schechter, “Stability conditions for nonlinear products and semigroups,” Pac. J. Math.,85, No. 1, 179–200 (1979).
E. Schechter, “Evolution generated by continuous dissipative plus compact operators,” Bull. London Math. Soc.,13, No. 4, 303–308 (1981).
R. Schönberg, Weak convergence of trajectories of nonexpansive semigroups on Hilbert space,” Isr. J. Math.,30, Nos. 1–2, 130–132 (1978).
S.-Y. Shaw, “Ergodic properties of continuous and discrete semigroups,” Proc. AMS,78, No. 1, 69–76 (1980).
S.-Y. Shaw, “Ergodic limits of tensor product semigroups,” J. Math. Anal. Appl.,76, No. 2, 432–439 (1980).
R. E. Showalter, Hilbert Space Methods for Partial Differential Equations, Pitman, London (1977).
R. E. Showalter, “Perturbation of maximal accretive operators with right angle,” Port. Math.,36, No. 2, 79–82 (1977).
B. Simon, “An abstract Kato's inequality for generators of positivity preserving semigroups,” Indiana Univ. Math. J.,26, No. 6, 1067–1073 (1977).
B. Simon, “Kato's inequality and the comparison of semigroups,” J. Funct. Anal.,32, No. 1, 97–101 (1979).
B. Simon and R. Hoegh-Krohn, “Hypercontractive semigroups and two dimension self-coupled Bose fields,” J. Funct. Anal.,9, No. 2, 121–180 (1972).
E. Sinestrati, “Accretive differential operators,” Boll. Unione Mat. Ital.,B13, No. 1, 19–31 (1976).
E. Sinestrati, “On the solutions of the homogeneous evolution equation in Banach spaces,” Rend. Accad. Naz. Lincei,70, No. 1, 12–17 (1981).
M. Slemrod, “The linear stabilization problem in Hilbert space,” J. Funct. Anal.,11, No. 3, 334–345 (1972).
M. Slemrod, “An application of maximal dissipative sets in control theory,” J. Math. Anal. Appl.,46, No. 2, 369–387 (1974).
M. Slemrod, “Asymptotic behavior of C0 semigroups as determined by the spectrum of the generator,” Indiana Univ. Math. J.,25, No. 8, 783–792 (1976).
M. Sova, “Unicité des solutions exponentielles des équations différentielles opérationnelles linéaires,” Boll. Unione Mat. Ital.,1, No. 6, 692–699 (1968).
M. Sova, “Régularite de l'évolution linéaire isochrone,” Czech. Mat. J.,20, No. 2, 251–302 (1970).
M. Sova, Linear Differential Equations in Banach Spaces, Rozpr. CSAV MPV,85, No. 6 (1975).
M. Sova, “On Hadamard's concepts of correctness,” Cas. Pestov. Mat.,102, No. 3, 234–269 (1977).
M. Sova, “Inhomogeneous linear differential equations in Banach spaces,” Cas. Pestov. Mat.,103, No. 2, 112–135 (1978).
M. Sova, “Abstract Cauchy problem,” Lect. Notes Math.,703, 384–396 (1979).
M. Sova, “The Laplace transform of analytic vector-valued functions (real conditions),” Cas. Pestov. Mat.,104, No. 2, 188–199 (1979).
M. Sova, “Concerning the characterization of generators of distribution semigroups,”. Cas. Pestov. Mat.,105, No. 4, 329–340 (1980).
M. Sova, Linear Differential Equations in Hilbert Spaces, Rozpr. CSAV MPV,91, No. 4 (1981).
H. B. Stewart, “Generation of analytic semigroups by strongly elliptic operators,” Trans. AMS,199, 141–162 (1974).
H. B. Stewart, “Generation of analytic semigroups by strongly elliptic operators under general boundary conditions,” Trans. AMS,259, No. 1, 299–310 (1980).
I. Straškraba and O. Vejvoda, “Periodic solutions to abstract differential equations,” Czech. Mat. J.,23, No. 4, 635–669 (1973).
P.-M. Suquet, “Evolution problems for a class of dissipative materials,” Q. Appl. Math.,38, No. 4, 391–414 (1981).
M. B. Tamburro, “The evolution operator solution of the Cauchy problem for the Hamilton-Jacobi equation,” Isr. J. Math.,26, Nos. 3–4, 232–264 (1977).
H. Tanabe, “On regularity of solutions of abstract differential equations,” in: Proc. Int. Conf. Funct. Anal. and Relat. Topics. Tokyo, 1969. Tokyo (1970), pp. 344–352.
H. Tanabe, Equation of Evolution, Pitman, London (1979).
H. Tanabe, “Differentiability of solutions of some unilateral problems of parabolic type,” J. Math. Soc. Jpn.,33, No. 3, 367–403 (1981).
M. Taniguti, Y. Takahashi, and H. Abe, “On the asymptotic behavior of asymptotically nonexpansive semigroups in Banach spaces,” Proc. Jpn. Acad.,A57, No. 3, 171–175 (1981).
Y. Temam, “Behavior at time t=0 of the solutions of semilinear evolution equations,” J. Diff. Equat.,43, No. 1, 73–92 (1982).
C. C. Travis, “Differentiability of weak solutions to an abstract inhomogeneous differential equation,” Proc. AMS,82, No. 3, 425–430 (1981).
R. Triggiani, “On the stabilizability problem in Banach space,” J. Math. Anal. Appl.,52, No. 3, 383–403 (1975).
H. F. Trotter, “Approximation and perturbation of semigroups,” in: Int. Ser. Numer. Math., Vol. 25, Basel-Stuttgart (1974), pp. 3–21.
M. Turinici, “Flow-invariance theorems via maximal element techniques,” Proc. Kon. Ned. Akad. Wetensch.,184, No. 4, 445–457 (1981).
M. Turinici, “Stability criteria for contractive semigroups via maximality procedures,” Bull. Austral. Math. Soc.,24, No. 3, 453–469 (1981).
T. Ushijima, “Some properties of regular distribution semigroups,” Proc. Jpn. Acad.,45, No. 4, 224–227 (1969).
T. Ushijima, “On the strong continuity of distribution semigroups,” J. Fac. Sci. Univ. Tokyo, Ser. 1A,17, Nos. 1–2, 363–372 (1970).
T. Ushijima, “On the generation and smoothness of semigroups of linear operators,” J. Fac. Sci. Univ. Tokyo, Sec. 1A,19, No. 1, 65–127 (1972).
T. Ushijima, “Correction to ‘On the generation and smoothness of semigroups of linear operators’,” J. Fac. Sci. Univ. Tokyo, Sec. 1A,20, No. 1, 187–189 (1973).
T. Ushijima, “Approximation theory for semigroups of linear operators and its application to approximation of wave equations,” Jpn. J. Math., New Ser.,1, No. 1, 185–224 (1975).
R. B. Vinter, “Semigroups on product spaces with application to initial value problems with nonlocal boundary conditions,” in: Contr. Distrib. Parameter Syst. Proc. 2nd IFAC Symp., Coventry, 1977. Oxford (1978), pp. 91–98.
J. Voigt, “On the perturbation theory for strongly continuous semigroups,” Math. Ann.,229, No. 2, 163–171 (1977).
I. I. Vrabie, “The nonlinear version of Pazy's local existence theorem,” Isr. J. Math.,32, Nos. 2–3, 221–235 (1979).
I. I. Vrabie, “Compactness methods and flow-invariance for perturbed nonlinear semigroups,” An. Sti. Univ. Iasi, Sec. 1a,27, No. 1, 117–125 (1981).
I. I. Vrabie, “Une méthode de compacité pour une classe d'équations d'évolution non linéaires,” C. R. Acad. Sci., Ser. 1,293, No. 2, 151–153 (1981).
I. I. Vrabie, “An existence result for a class of nonlinear evolution equations in Banach spaces,” Nonlinear Anal.: Theory, Meth. Appl.,6, No. 7, 711–722 (1982).
J. Watanabe, “On certain nonlinear evolution equations,” J. Math. Soc. Jpn.,25, No. 3, 446–463 (1973).
M. Watanabe, “On the characterisation of semigroups of linear operators,” Sci. Repts. Niigata Univ., A, No. 10, 43–50 (1973).
M. Watanabe, “Convergence and approximation of integral solutions of nonlinear evolution equations,” Proc. Jpn. Acad.,A54, No. 9, 269–273 (1978).
G. F. Webb, “Continuous nonlinear perturbations of linear accretive operators in Banach spaces,” J. Funct. Anal.,10, No. 2, 191–203 (1972).
G. F. Webb, “Nonlinear perturbations of linear accretive operators in Banach spaces,” Isr. J. Math.,12, No. 3, 237–248 (1972).
G. F. Webb, “Regularity of solutions to an abstract inhomogeneous linear differential equation,” Proc. AMS,62, No. 2, 271–277 (1977).
G. F. Webb, “Compactness of bounded trajectories of dynamical systems in infinite dimensional spaces,” Proc. R. Acad. Edinburgh,A84, Nos. 1–2, 19–33 (1979).
J. Weilenmann, “Continuity properties of fractional powers of the logarithm, and of holomorphic semigroups,” J. Funct. Anal.,27, No. 1, 1–20 (1978).
J. Weilenmann, “An approximation theorem for linear Cauchy problems in Banach space,” J. Funct. Anal.,27, No. 1, 21–37 (1978).
F. B. Weissler, “Logarithmic Sobolev inequalities for the heat-diffusion semigroup,” Trans. AMS,237, 255–269 (1978).
F. B. Weissler, “Construction of nonlinear semigroups using product formulas,” Isr. J. Math.,29, Nos. 2–3, 265–275 (1978).
F. B. Weissler, “Two-point inequalities, the Hermite semigroup, and the Gauss-Weierstrass semigroup,” J. Funct. Anal.,32, No. 1, 102–121 (1979).
U. Westphal, “On approximation by semigroups of nonlinear contractions. I,” J. Approxim. Theory,13, No. 3, 205–217 (1975).
U. Westphal, “On approximation by semigroups of nonlinear contractions. II,” J. Approxim. Theory,15, No. 1, 11–17 (1975).
D. Wexler, “Nonlinear passive evolution equations,” J. Diff. Equat.,23, No. 3, 414–435 (1977).
C. Wild, “Domaines de p-crossance d'un semigroupe d'opérateurs sur un espace de Banach,” C. R. Acad. Sci.,A279, No. 2, 57–59 (1974).
C. Wild, “Semigroupes de classe p,” C. R. Acad. Sci.,280, No. 23, A1595-A1598 (1975).
C. Wild, “Semigroupes de class p avec poids,” C. R. Acad. Sci.,282, No. 18, A1087-A1090 (1976).
C. Wild, “Semigroupes distribution de classe p,” C. R. Acad. Sci.,282, No. 19, A1147-A1149 (1976).
C. Wild, “Semigroupes de croissance α<1 holomorphes,” C. R. Acad. Sci.,A285, No. 6, A437-A440 (1977).
N. Yamada, “On a nonlinear noncontractive semigroup,” Proc. Jpn. Acad.,52, No. 3, 102–105 (1976).
Y. Yamada, “On evolution equations generated by subdifferential operators,” J. Fac. Sci. Univ. Tokyo, Sec. 1A,23, No. 3, 491–515 (1976).
Y. Yamada, “Quasilinear wave equations and related nonlinear evolution equations,” Nagoya Math. J.,84, 31–83 (1981).
A. Yamamoto and N. Okazawa, “Weakly closed m-accretive operators,” Proc. AMS,66, No. 2, 284–288 (1977).
A. Yoshikawa, “Note on singular perturbation of linear operators,” Proc. Jpn. Acad.,48, No. 8, 595–598 (1972).
A. Yoshikawa, “On perturbation of closed operators in a Banach space,” J. Fac. Sci. Hokkaido Univ., Ser. 1,22, Nos. 1–2, 50–61 (1972).
S. Yotsutani, “Evolution equations associated with the subdifferentials,” J. Math. Soc. Jpn.,31, No. 4, 623–646 (1979).
J. Zabczyk, “A note on C0-semigroups,” Bull. Acad. Pol. Sci. Ser. Sci. Math., Astron. Phys.,23, No. 8, 895–898 (1975).
S. Zaidman, “Spectrum of almost-periodic solutions for some abstract differential equations,” J. Math. Anal. Appl.,28, No. 2, 336–338 (1969).
S. Zaidman, “Uniqueness of bounded solutions for some abstract differential equations,” Ann. Univ. Ferrara, Sez. 7,14, No. 10, 101–104 (1969).
S. Zaidman, “Uniqueness of bounded weak solutions for some abstract differential equations,” Ann. Univ. Ferrara, Sez. 7,14, No. 9, 97–100 (1969).
S. Zaidman, “Bounded solutions of some abstract differential equations,” Proc. AMS,23, No. 2, 340–342 (1969).
S. Zaidman, “Remarks on weak solutions of differential equations in Banach spaces,” Boll. Unione Mat. Ital.,4, No. 2, 615–637 (1969).
S. Zaidman, “On elementary solutions of abstract differential equations,” Boll. Unione Mat. Ital.,2, Nos. 4–5, 487–490 (1969).
S. Zaidman, “On some almost-periodic functions,” Ann. Univ. Ferrara, Ser. 7,14, No. 5, 29–34 (1969).
S. Zaidman, “An existence theorem for bounded vector-valued functions,” Ann. Scuola Norm. Super. Sci. Fis. Mat.,24, No. 1, 85–89 (1970).
S. Zaidman, “Some asymptotic theorems for abstract differential equations,” Proc. AMS,25, No. 3, 521–525 (1970).
S. Zaidman, “Some results on almost-periodic differential equations,” Rend. Semin. Math. Fis. Milano,41, 137–142 (1971).
S. Zaidman, “On a certain approximation property for first-order abstract differential equations,” Rend. Sem. Mat. Univ. Padova,46, 191–198 (1971(1972)).
S. Zaidman, “Remarks on regularity theorems for weak solutions of abstract differential equations,” Boll. Unione Mat. Ital.,6, No. 1, 55–60 (1972).
S. Zaidman, “Remarks on boundedness of solutions of abstract differential equations,” Ann. Univ. Ferrara, Sez. 7,17, No. 5, 43–45 (1972).
S. Zaidman, “Remarks on weak solutions of differential equations in Banach spaces,” Boll. Unione Mat. Ital.,9, 638–643 (1974).
Z. Zaidman, “Structure of bounded solutions for a class of abstract differential equations,” Ann. Univ. Ferrara, Sez. 7,22, 43–47 (1976).
S. Zaidman, “A regularity property of abstract differential equations,” Rend. Ist. Lombardo. Accad. Sci. Lett.,A110, No. 1, 74–79 (1976).
S. Zaidman, “Solutions presque-periodiques des equations differentielles abstraites,” Enseign. Math.,24, Nos. 1–2, 87–110 (1978).
S. Zaidman, “Almost-automorphic solutions of some abstract evolution equations,” Rend. Ist. Lombardo. Accad. Sci. Lett.,A110, No. 2, 578–588 (1976).
S. Zaidman, “The weak Cauchy problem for abstract differential equations,” Rend. Sem. Mat. Univ. Padova,56, 1–21 (1976).
S. Zaidman, “On optimal mild solutions of nonhomogeneous differential equations in Banach spaces,” Proc. R. Soc. Edinburgh,A84, Nos. 3–4, 273–277 (1979).
S. Zaidman, “Abstract differential equations,” Rez. Notes Math., No. 36, (1979).
S. Zaidman, “Remarks on the well-posed weak Cauchy problem,” Boll. Unione Mat. Ital.,B17, No. 3, 1012–1022 (1980).
S. Zaidman, “Some remarks concerning regularity of solutions for abstract differential equations,” Rend. Sem. Mat. Univ. Padova,62, 47–64 (1980).
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Translated from Itogi Nauki i Tekhniki, Seriya Matematicheskii Analiz, Vol. 21, pp. 130–264, 1983.
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Krein, S.G., Khazan, M.I. Differential equations in a Banach space. J Math Sci 30, 2154–2239 (1985). https://doi.org/10.1007/BF02105398
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DOI: https://doi.org/10.1007/BF02105398