In this paper we consider Neumann noncoercive hemivariational inequalities, focusing on nontrivial solutions. We use the critical point theory for locally Lipschitz functionals.
We study the quasilinear elliptic problem with multivalued terms.We consider the Dirichlet problem with a multivalued term appearing in the equation and a problem of Neumann type with a multivalued term appearing in the boundary condition. Our approach is based on Szulkin’s critical point theory for lower semicontinuous energy functionals.