# American Institute of Mathematical Sciences

June  2017, 6(2): 277-297. doi: 10.3934/eect.2017015

## Periodic solutions for time-dependent subdifferential evolution inclusions

 1 National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, Greece 2 Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia 3 Institute of Mathematics "Simion Stoilow" of the Romanian Academy, P.O. Box 1-764,014700 Bucharest, Romania

* Corresponding author:Vicenţiu D.Rădulescu

Received  May 2016 Revised  January 2017 Published  April 2017

We consider evolution inclusions driven by a time dependent subdifferential plus a multivalued perturbation. We look for periodic solutions. We prove existence results for the convex problem (convex valued perturbation), for the nonconvex problem (nonconvex valued perturbation) and for extremal trajectories (solutions passing from the extreme points of the multivalued perturbation). We also prove a strong relaxation theorem showing that each solution of the convex problem can be approximated in the supremum norm by extremal solutions. Finally we present some examples illustrating these results.

Citation: Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu. Periodic solutions for time-dependent subdifferential evolution inclusions. Evolution Equations & Control Theory, 2017, 6 (2) : 277-297. doi: 10.3934/eect.2017015
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