Anti-periodic extremal problems for a class of nonlinear evolution inclusions in

The aim of this paper is to establish the existence of anti-periodic solutions to the following nonlinear anti-periodic problem: a.e. , , in where denotes the extremal point set of the multifunction , and is a nonlinear map from to . Sufficient conditions for the existence of extremal solutions are presented. Also, we prove that the extremal point set of this problem is compact in and dense in the solution set of nonlinear evolution problems with a convex valued perturbation which is multivalued. We apply our results on the control system with a priori feedback.