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