Periodic solutions  for differential inclusions in $\mathbb {R}^N$

M. E. Filippakis, N. S. Papageorgiou

Department of Mathematics, School of Applied Mathematics and Natural Science, National Technical University, Zografou Campus, Athens 15780, Greece



We consider first order periodic differential inclusions in  $\mathbb{R}^N$. The presence of a subdifferential term  incorporates in our framework differential variational  inequalities in $\mathbb{R}^N$. We establish the existence of extremal periodic solutions and we also obtain existence results  for the ``convex'' and ``nonconvex''problems.


AMSclassification. 34A60.

Keywords. Multifunction, convex subdifferential, extremal periodik solution, Moreanu-Yosida approximation.