Discontinuous quasilinear elliptic problems at resonance

Nikolaos Kourogenis; Nikolaos Papageorgiou

ArticleOriginal scientific text

Title

Discontinuous quasilinear elliptic problems at resonance

Authors ¹, ²

Affiliations

Department of Mathematics National Technical University Zografou Campus Athens 157 80, Greece
Department of Mathematics, National Technical University, Zografou Campus, Athens 157 80, Greece

Abstract

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.

Keywords

ENG

compact embedding, Poincaré's inequality, Palais-Smale condition, critical point, variational method, Mountain Pass Theorem, subdifferential, problems at resonance, locally Lipschitz functional

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Title

Discontinuous quasilinear elliptic problems at resonance

Affiliations

Abstract

Keywords

Bibliography