This is a preview of subscription content, log in via an institution to check access.
References
V. Barbu, A class of boundary problems for second order abstract differential equations,J. Fac. Sci. Univ. Tokyo I A Math.,19 (1972), 295–319.
V. Barbu,Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff International (Leyden. The Netherlands, 1975).
G. Da Prato andE. Giusti, Una caratterizzazione dei generatori di funzioni coseno astratte,Boll. Unione Mat. Italiana. 22 (1967), 357–362.
N. Dunford andJ. T. Schwartz,Linear Operators, Part I: General Theory, Interscience (New York, 1958).
H. O. Fattorini, Ordinary differential equations in linear topological spaces, I,J. Differential Equations,5 (1968), 72–105.
H. O. Fattorini, Ordinary differential equations in linear topological spaces, II,J. Differential Equations,6 (1969), 50–70.
H. O. Fattorini, Uniformly bounded cosine functions in Hilbert space,Indiana Univ. Math. J.,20 (1970), 411–425.
E. Giusti, Funzioni coseno periodiche,Boll. Unione Mat. Italiana,22 (1967), 478–485.
J. Goldstein, Semi-groups and hyperbolic equations,J. Functional Analysis,4 (1969), 50–70.
J. Goldstein, On a connection between first and second order differential equations in Banach spaces.J. Math. Anal. Appl.,30 (1970), 246–251.
J. Goldstein, On the convergence and approximation of cosine functions,Aequationes Math.,11 (1974), 201–205.
J. Goldstein,Semigroups of Operators and Abstract Cauchy Problems, Monograph, Tulane University (New Orleans, 1970).
T. Kato,Perturbation Theory for Linear Operators, Springer-Verlag (New York, 1966).
J. Kisyński, On operator-valued solutions of d'Alembert's functional equation, I,Colloquium Math.,23 (1971), 107–114.
Y. Konishi, Cosine functions of operators in locally convex spaces,J. Fac. Sci. Univ. Tokyo I. A. Math.,18 (1971/72), 443–463.
S. G. Krein,Lienar Differential Equations in Banach Spaces, Amer. Math. Soc. Translations of Math. Monographs, Vol.29 (Providence, 1971).
S. Kurepa, On some functional equations in Banach spaces,Studia Math.,19 (1960), 149–158.
S. Kurepa, A cosine funcational equation in Banach algebras,Acta Sci. Math. Szeged,23 (1962), 255–267.
V. Lakshmikantham,Differential Equations in Abstract Spaces, Academic Press (New York, 1972).
B. Nagy, On the generators of cosine operator functions,Publ. Math. Debrecen,21 (1974), 151–154.
B. Nagy, On cosine operator functions in Banach spaces,Acta Sci. Math. Szeged,36 (1974), 281–289.
B. Nagy, Cosine operator functions and the abstract Cauchy problem,Periodica Math. Hungar.,7(3) (1976), 15–18.
I. Segal, Non-linear semi-groups,Ann. Math.,78 (1963), 339–364.
M. Sova, Cosine operator functions,Rozprawy Matematiyczne,49 (1966), 1–47.
M. Sova, Semigroups and cosine functions of normal operators in Hilbert spaces,Časopis Pěst. Mat.,93 (1968), 437–458.
C. Travis andG. Webb, Existence and stability for partial functional differential equations,Trans. Amer. Math. Soc.,200 (1974), 395–418.
K. Yosida,Functional Analysis, Fourth Ed., Springer-Verlag (New York, 1974).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Travis, C.C., Webb, G.F. Cosine families and abstract nonlinear second order differential equations. Acta Mathematica Academiae Scientiarum Hungaricae 32, 75–96 (1978). https://doi.org/10.1007/BF01902205
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01902205