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Multiplicity theorems for semilinear elliptic problems depending on a parameter

Part of: Elliptic equations and systems Variational problems in infinite-dimensional spaces

Published online by Cambridge University Press:  02 February 2009

Alexandru Kristály  and
Nikolaos S. Papageorgiou
Alexandru Kristály
Affiliation:
Department of Economics, University of Babeş-Bolyai, 400591 Cluj Napoca, Romania (alexandrukristaly@yahoo.com)
Nikolaos S. Papageorgiou
Affiliation:
2Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece (npapg@math.ntua.gr)
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Abstract

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We consider semilinear elliptic problems in which the right-hand-side nonlinearity depends on a parameter λ > 0. Two multiplicity results are presented, guaranteeing the existence of at least three non-trivial solutions for this kind of problem, when the parameter λ belongs to an interval (0,λ*). Our approach is based on variational techniques, truncation methods and critical groups. The first result incorporates as a special case problems with concave–convex nonlinearities, while the second one involves concave nonlinearities perturbed by an asymptotically linear nonlinearity at infinity.

Keywords

critical pointlocal minimizertruncated functionalcritical groups

MSC classification

Secondary: 35J20: Variational methods for second-order elliptic equations 35J60: Nonlinear elliptic equations 58E50: Applications
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 1 , February 2009 , pp. 171 - 180
Copyright
Copyright © Edinburgh Mathematical Society 2009