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

*M. E. Filippakis,
N. S. Papageorgiou*

**Address****.**

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

**E-mail: **mfilip@math.ntua.gr, npapg@math.ntua.gr

**Abstract****.**

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.