EXISTENCE OF SOLUTIONS FOR A CLASS OF HISTORY-DEPENDENT EVOLUTION HEMIVARIATIONAL INEQUALITIES

We deal with a class of abstract second order evolution inclusions involving a nonlinear history-dependent operator. For this class we prove an existence and uniqueness result. The proof is based on arguments of evolution inclusions with monotone operators and the Banach fixed point theorem. We apply this result to prove the solvability of a class of second order hemivariational inequalities with nonlinear memory term and, under an additional assumption, its unique solvability.