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.