Multiplicity theorems for semilinear elliptic problems depending on a parameter

A. Kristály, Nikolaos S. Papageorgiou

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 2009

Fingerprint

Semilinear Elliptic Problem
Multiplicity
Nonlinearity
Theorem
Critical Group
Asymptotically Linear
Multiplicity Results
Nontrivial Solution
Truncation
Infinity
Interval

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Multiplicity theorems for semilinear elliptic problems depending on a parameter. / Kristály, A.; Papageorgiou, Nikolaos S.

In: Proceedings of the Edinburgh Mathematical Society, Vol. 52, No. 1, 02.2009, p. 171-180.

Research output: Contribution to journalArticle

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