Periodic solutions for semi-linear evolution inclusions

In this paper, we study the periodic problem for semi-linear evolution inclusion. Using techniques from multivalued analysis and fixed point theorems, we establish existence theorems under the one-sided Lipschitz condition. First we prove existence theorems for nonconvex and convex problem. Second, we look for extremal periodic solutions and prove the relaxation theorem. © 2006 Elsevier Inc. All rights reserved