### Multiple solutions for nonlinear discontinuous elliptic problems near resonance

Nikolaos Kourogenis, Nikolaos Papageorgiou (1999)

Colloquium Mathematicae

Similarity:

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 $\lambda \to {\lambda}_{1}$ from the left, ${\lambda}_{1}$ being the principal eigenvalue of the p-Laplacian with the Dirichlet boundary conditions.