On Nontrivial Solutions of Variational-Hemivariational Inequalities with Slowly Growing Principal Parts

Abstract

This paper is concerned with the inclusion

with Dirichlet boundary condition $u=0$ on $\partial \Omega$, in the case where the higher order part has slow growth and the lower order part is locally Lipschitz. By using a Mountain Pass theorem for variational-hemivariational inequalities without the Palais–Smale condition in Orlicz–Sobolev spaces, we show the existence of nontrivial solutions of the above inclusion.