Existence results for evolution hemivariational inequalities of second order

In this paper, we consider evolution hemivariational inequalities of second order with a time-dependent pseudomonotone operator and nonmonotone multivalued perturbations. We present the existence of solutions for such inequality. The proof profits from a result on the surjectivity of operators of pseudomonotone type. We discuss some examples which indicate the practical importance of our theoretical findings.