Multiplicity theorems for semilinear elliptic problems depending on a parameter

Alexandru Kristály, Nikolaos S. Papageorgiou

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Abstract

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

Original languageEnglish
Pages (from-to)171-180
Number of pages10
JournalProceedings of the Edinburgh Mathematical Society
Volume52
Issue number1
DOIs
Publication statusPublished - Feb 1 2009

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Keywords

  • Critical groups
  • Critical point
  • Local minimizer
  • Truncated functional

ASJC Scopus subject areas

  • Mathematics(all)

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