Existence results for semilinear elliptical hemivariational inequalities

We are interested in studying the existence of solutions to an elliptical hemivariational inequality, depending on a real parameter λ$\lambda$. The main tool in the proof of our results is a critical point theorem recently established. We obtain the existence of solution through a direct method, both with a changing sign nonlinearity of the kind p(x)f(ξ)$p\left(x\right)f\left(\xi \right)$ and in the classical one P(x,ξ)$P(x,\xi )$ too.