Hemivariational Inequalities with a general growth condition: Existence and Approximation

The article deals with the existence and the approximation of nontrivial solutions to a general hemivariational inequality where the potential corresponding to the nonlinear term admits a superquadratic growth. Finally, convergence results for Galerkin type approximation are established. Since the usual techniques based on coerciveness assumptions fail in this case, one makes use of nonsmooth variational arguments. Our approach allows to cover in a unifying way the superlinear and sublinear situations. Improvements and completions of previous results are obtained.