Multiplicity results to a class of variational-hemivariational inequalities

Abstract

This paper deals with variational-hemivariational inequalities involving the $p$-Laplace operator and a nonlinear Neumann boundary condition. Based on an abstract critical point result, which is developed at the beginning of the paper, it is shown the existence of at least three solutions to such inequalities whereby the cases $p> N$ and $p \leq N$ are treated separately. The applicability of these results is emphasized with suitable examples.