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Multiple solutions for semilinear elliptic problems

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  26 February 2010

Martin Schechter
Martin Schechter
Affiliation:
Department of Mathematics, University of California, Irvine, CA 92697-3875, U.S.A.
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Abstract

A method of finding critical points in a half space is developed. It is then applied to the study of semilinear boundary value problems, and used to determine conditions which lead to multiple non-trivial solutions.

MSC classification

Secondary: 35J65: Nonlinear boundary value problems for linear elliptic equations
Type
Research Article
Information
Mathematika , Volume 47 , Issue 1-2 , December 2000 , pp. 307 - 317
Copyright
Copyright © University College London 2000

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References

1.Alama, S. and Tarantello, G.. On semilinear elliptic equations with indefinite nonlinearities. Calculus of Variations, 1 (1993), 439–475.Google Scholar
2.Ahmad, S., Lazer, A. C. and Paul, J.. Elementary critical point theory and perturbations of elliptic boundary value problems at resonance. Indiana Univ. Math. J., 25 (1976), 933–944.CrossRefGoogle Scholar
3.Chang, K.-C.. Infinite-dimensional Morse theory and multiple solution problems. In Progress in Nonlinear Differential Equations and their Applications (Birkhäuser, Boston, 1993).Google Scholar
4.Castro, A. and Lazer, A. C.. Critical point theory and the number of solutions of a nonlinear Dirichlet problem. Ann. Mat. Pura Appl. (4), 120 (1979), 113–137.CrossRefGoogle Scholar
5.Costa, D. G. and Magalhães, C. A.. Variational elliptic problems which are nonquadratic at infinity. Trabelhos Mat., 250 (1991), 1–14.Google Scholar
6.Costa, D. G. and Magalhães, C. A.. Un probleme elliptique nonquadratique a linfini. C. R. Acad. Sci. Paris, 315 (1992), 1059–1062.Google Scholar
7.Figueiredo, D. G. de and Massabo, I.. Semilinear elliptic equations with primitive of the nonlinearity interacting with the first eigenvalue. J. Math. Anal. Appl., 156 (1991), 381–394.CrossRefGoogle Scholar
8.Gonçalves, J. V., Padua, J. C. de and Carrião, P. C.. Variational elliptic problems at double resonance. Differential Integral Equations, 9 (1996), 295–303.Google Scholar
9.Landesman, E. A. and Lazer, A. C.. Nonlinear perturbations of linear elliptic boundary value problems at resonance. J. Math. Mech., 19 (1970), 609–623.Google Scholar
10.Lazer, A. C. and McKenna, P. J.. Critical point theory and boundary value problems with nonlinearities crossing multiple eigenvalues, I. Comm. P. D. E. 10 (1985), 107–150; II. J. Math. Mech., 11 (1986), 1653–1676.CrossRefGoogle Scholar
11.Schechter, M.. The intrinsic mountain pass. Pacific J. Math., 171 (1995), 529–544.CrossRefGoogle Scholar
12.Schechter, M.. Critical points when there is no saddle point geometry. Topol. Methods Nonlinear Anal., 6 (1995), 295–308.CrossRefGoogle Scholar
13.Schechter, M.. Linking Methods in Critical Point Theory (Birkäuser, Boston, 1999).CrossRefGoogle Scholar
14.Schechter, M.. A bounded mountain pass lemma without the (PS) condition and applications. Trans. Amer. Math. Soc. 331 (1992), 681–703.CrossRefGoogle Scholar
15.Schechter, M. and Tintarev, K.. Pairs of critical points produced by linking subsets with applications to semilinear elliptic problems. Bull. Soc. Math. Belg., 44 (1992), 249–261.Google Scholar
16.Silva, E. A. de B. e.. Linking theorems and applications to semilinear elliptic problems at resonance. Nonlinear Analysis TMA, 16 (1991), 455–477.CrossRefGoogle Scholar