On nontrivial solutions of variational-hemivariational inequalities with slowly growing principal parts (Q732873)

Summary: This paper is concerned with the inclusion \[ -\text{div} \big(a(|\nabla u|)\nabla u\big)+ \partial_uG(x,u)\ni 0\quad\text{in }\Omega, \] 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.