On a class of hemivariational inequalities at resonance

We consider a class of noncoercive hemivariational inequalities involving the p-Laplacian at resonance. We use the unilateral growth condition so the energy functional is nonsmooth, nonconvex and its effective domain does not coincide with the whole space W 1,p 0 (Ω). To avoid this difficulty we study the problem in finite-dimensional spaces using the mountain-pass theorem for locally Lipschitz functionals and then we pass to the limit to obtain the existence of solutions.  2003 Elsevier Inc. All rights reserved.