Existence of Anti-Periodic Solutions for a Class of First Order Evolution Inclusions

Xiaoyou Liu, Yiliang Liu

The existence of anti-periodic solutions for a class of first order nonlinear evolution inclusions defined in the framework of an evolution triple of spaces is considered. We study the problems under both convexity and nonconvexity conditions on the multivalued right-hand side. The main tools in our study are the maximal monotone property of the derivative operator with anti-periodic conditions, the surjectivity result for $L$-pseudomonotone operators and continuous extreme selection results from multivalued analysis. An example of a nonlinear parabolic problem is given to illustrate our results.