Existence results for semilinear elliptical hemivariational inequalities

We are interested in studying the existence of solutions to anelliptic hemivariational inequality, depending on a real parameter$lambda$. The main tool in the proof of our results is a criticalpoint theorem recently established. We obtain the existence ofsolution through a direct method, both with a changing signnonlinearity of the kind $p(x)f(\xi)$ and in the classical one$P(x,\xi)$ too.