A class of differential hemivariational inequalities constrained on nonconvex star-shaped sets

The purpose of this paper is to investigate a class of nonconvex constrainted differential hemivariational inequalities consisting of nonlinear evolution equations and evolutionary hemivariational inequalities. The admissible set of constraints is closed and star-shaped with respect to a certain ball in a reflexive Banach space. We construct an auxiliary inclusion problem and obtain the existence results by applying a surjectivity theorem for multivalued pseudomonotone operators and the properties of Clarke subgradient operator. Moreover, the existence of solution of original problem is established by hemivariational inequality approach and a penalization method in which a small parameter does not have to tend to zero. Finally, an application of the main results is provided.