Existence theorems for elliptic hemivariational inequalities involving the $p$-Laplacian

Abstract

We study quasilinear hemivariational inequalities involving the $p$-Laplacian. We prove two existence theorems. In the first, we allow “crossing” of the principal eigenvalue by the generalized potential, while in the second, we incorporate problems at resonance. Our approach is based on the nonsmooth critical point theory for locally Lipschitz energy functionals.