On existence of solutions for parabolic hemivariational inequalities

A class of parabolic hemivariational inequalities is considered in which the energy function is locally Lipschitz (not necessarily convex or differentiable) and the nonlinear evolution operator is multivalued and generalized pseudomonotone. Using techniques of multivalued analysis and a surjectivity result for L-generalized pseudomonotone operators, we prove the existence for a Cauchy problem and a periodic problem. Some applications to nonsmooth mechanics are also indicated.