Multiple solutions for nonlinear discontinuous elliptic problems near resonance

Nikolaos Kourogenis; Nikolaos Papageorgiou

Displaying similar documents to “Multiple solutions for nonlinear discontinuous elliptic problems near resonance”

Existence and multiplicity results for nonlinear eigenvalue problems with discontinuities

Nikolaos Papageorgiou, Francesca Papalini (2000)

Annales Polonici Mathematici

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We study eigenvalue problems with discontinuous terms. In particular we consider two problems: a nonlinear problem and a semilinear problem for elliptic equations. In order to study the existence of solutions we replace these two problems with their multivalued approximations and, for the first problem, we estabilish an existence result while for the second problem we prove the existence of multiple nontrivial solutions. The approach used is variational.

Discontinuous quasilinear elliptic problems at resonance

Nikolaos Kourogenis, Nikolaos Papageorgiou (1998)

Colloquium Mathematicae

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In this paper we study a quasilinear resonant problem with discontinuous right hand side. To develop an existence theory we pass to a multivalued version of the problem, by filling in the gaps at the discontinuity points. We prove the existence of a nontrivial solution using a variational approach based on the critical point theory of nonsmooth locally Lipschitz functionals.