This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
H. Brezis, Équations et in équations non-lineares dans les espaces en dualité, Ann. Inst. Fourier, Grenoble, 18 (1968), 115–175.
F.E. Browder, Existence theory for boundary value problems for quasilinear elliptic systems with strongly nonlinear lower order terms, Proc. Symp. in Pure Math. 23 (1973), 269–286.
_____, Nonlinear operators and nonlinear equations of evolution in Banach spaces, Proc. Symp. in Pure Math, AMS, Vol. 18, Part 2 (1976).
F.E. Browder and W.V. Petryshyn, Approximation methods and the generalized topological degree for nonlinear maps in Banach spaces, J. Functional Anal., 3 (1969), 217–245.
K.J. Brown, Some operator equations with an infinite number of solutions, Quart. J. Math (Oxford) (2), 25 (1974), 195–212.
B. Calvert and J.R.L. Webb, An existence theorem for quasimonotone operators, Accad. Naz. Dei Lincei, Ser. 8, 50 (1971), 362–368.
E.N. Dancer, Boundary-value problems for ordinary differential equations on infinite intervals, Proc. London Math. Soc. 30 (1975), 76–94.
N. Dunford and J.T. Schwartz, Linear Operators, Part II; Interscience, New York, 1963.
P.M. Fitzpatrick, Surjectivity results for nonlinear mappings from a Banach space to its dual, Math. Ann. 204 (1973), 177–188.
P.M. Fitzpatrick and W.V. Petryshyn, Positive eigenvalues for nonlinear multivalued noncompact operators with applications to differential operators, J. Differential Equations, 22 (1976), 428–441.
D.G. De Figueiredo, The Dirichlet problem for nonlinear elliptic equations: A Hilbert space approach
A. Friedman, Partial Differential Equations, Holt, Rinehart and Winston, New York, 1969.
P. Hess, On nonlinear mappings of monotone type homotopic to odd operators, J. Functional Anal., 11 (1972), 138–167.
P.M. Hess, Théorème d'existence pour des perturbations d'opérateurs maximaux monotones, C.R. Acad. Sc. Paris, t.275 (1972), Ser. A, 1171–1173.
J. Leray and J.-L. Lions, Quelques résultats de Višik sur les problemes elliptiques non linéaires par les méthodes de Minty-Browder, Bull. Soc. Math. Frances 93 (1965), 97–107.
P.S. Milojevic and W.V. Petryshyn, Continuation and surjectivity theorems for uniform limits of A-proper mappings with applications, J. Math. Anal. Appl. (to appear).
_____, Continuation theorems and the approximation-solvability of equations involving multivalued A-proper mappings, J. Math. Anal. Appl. (to appear).
G. Minty, Monotone (nonlinear) operators in Hilbert space, Duke Math. J. 29 (1962), 341–346.
R.D. Nussbaum, The fixed point index for local condensing maps, Ann. Math. Pura Appl. (4) 89 (1971), 217–258.
W.V. Petryshyn, On nonlinear equations involving pseudo-A-proper mappings and their uniform limits with applications, J. Math. Anal. Appl. 38 (1972), 672–720.
_____, On the approximation-solvability of equations involving A-proper and pseudo-A-proper mappings, Bull. Amer. Math. Soc., 81 (1975), 223–312.
_____, On the relationship of A-properness to mappings of monotone type with applications to elliptic equations, Fixed Point Theory and its Application (ed. S. Swaminathan), Academic Press, N.Y.), 1976, 149–174.
_____, Fixed point theorems for various classes of 1-set-contractive and 1-ball-contractive mappings in Banach spaces, Trans. Amer. Math. Soc. 182 (1973), 323–352.
_____, Fredholm alternative for nonlinear A-proper mappings with applications to nonlinear elliptic boundary value problems, J. Functional Anal. 18 (1975), 288–317.
W.V. Petryshyn and P.M. Fitzpatrick, On 1-set and 1-ball contractions with applications to perturbation problems for nonlinear bijective maps and linear Fredholm maps, Bull. UMI, (4) 7 (1973), 102–124.
B.N. Sadovskii, Ultimately compact and condensing mappings, Uspehi Mat. Nauk 27 (1972), 81–146.
C.A. Stuart, Some bifurcation theory for k-set-contractions, Proc. London Math. Soc. 27 (1973), 531–550.
J.F. Toland, Global bifurcation theory via Galerkin method, University of Essex, Fluid Mechanics Reas. Inst. Report. No. 69 (1976).
M.M. Vainberg, Variational Methods for the Study of Nonlinear Operators, Holden-Day, San Francisco, 1964.
J.R.L. Webb, Mapping and fixed point theorems for nonlinear operators in Banach spaces, Proc. London Math. Soc. (3) 20 (1970), 451–468.
J.R.L. Webb, On a characterization of k-set-contractions, Accad. Naz. Dei Lincei, Ser. 8, 50 (1971), 358–361.
F. Wille, Monotone Operatoren mit Störungen, Arch. Rat. Mech. Anal. 46 (1971), 369–388.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1979 Springer-Verlag
About this paper
Cite this paper
Petryshyn, W.V. (1979). On the solvability of nonlinear equations involving abstract and differential operators. In: Nashed, M.Z. (eds) Functional Analysis Methods in Numerical Analysis. Lecture Notes in Mathematics, vol 701. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062083
Download citation
DOI: https://doi.org/10.1007/BFb0062083
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09110-3
Online ISBN: 978-3-540-35530-4
eBook Packages: Springer Book Archive