Optimal Control Problems Governed by Time Dependent Subdifferential Operators with Delay

This article is devoted to the study, in the infinite dimensional setting, of a Bolza-type problem governed by a class of functional evolution inclusion which involves a time-dependent subdifferential operator with a time-delay perturbation. We present a relaxation result associated with such equations where the controls are Young measures in order to show the existence of an optimal solution under a suitable convexity assumption.