Displaying similar documents to “A saddle point approach to nonlinear eigenvalue problems”

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.

Multiple solutions for nonlinear discontinuous elliptic problems near resonance

Nikolaos Kourogenis, Nikolaos Papageorgiou (1999)

Colloquium Mathematicae

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We consider a quasilinear elliptic eigenvalue problem with a discontinuous right hand side. To be able to have an existence theory, we pass to a multivalued problem (elliptic inclusion). Using a variational approach based on the critical point theory for locally Lipschitz functions, we show that we have at least three nontrivial solutions when λ → λ 1 from the left, λ 1 being the principal eigenvalue of the p-Laplacian with the Dirichlet boundary conditions.