Positive solutions and multiple solutions at non-resonance, resonance and near resonance for hemivariational inequalities with 𝑝-Laplacian

Abstract

In this paper we study eigenvalue problems for hemivariational inequalities driven by the p p -Laplacian differential operator. We prove the existence of positive smooth solutions for both non-resonant and resonant problems at the principal eigenvalue of the negative p p -Laplacian with homogeneous Dirichlet boundary condition. We also examine problems which are near resonance both from the left and from the right of the principal eigenvalue. For nearly resonant from the right problems we also prove a multiplicity result.