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

摘要

This paper is concerned with the inclusion -div(alpha(vertical bar del u vertical bar)del u) + partial derivative(u)G(x, u) (sic) 0 in Omega, with Dirichlet boundary condition u = 0 on partial derivative 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.