Multiple solutions for nonlinear discontinuous elliptic problems near resonance
Volume 81 / 1999
Colloquium Mathematicum 81 (1999), 89-99
DOI: 10.4064/cm-81-1-89-99
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 $λ → λ_1$ from the left, $λ_1$ being the principal eigenvalue of the p-Laplacian with the Dirichlet boundary conditions.
