ArticleOriginal scientific text

Title

Multiple solutions for nonlinear discontinuous elliptic problems near resonance

Authors 1, 1

Affiliations

  1. Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece

Abstract

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 λλ1 from the left, λ1 being the principal eigenvalue of the p-Laplacian with the Dirichlet boundary conditions.

Keywords

discontinuous function, generalized directional derivative, critical point, coercive functional, multiple solutions, Clarke subdifferential, Rayleigh quotient, first eigenvalue, p-Laplacian, elliptic inclusion, nonsmooth Palais-Smale condition

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Pages:
89-99
Main language of publication
English
Received
1998-09-16
Accepted
1999-01-28
Published
1999
Exact and natural sciences