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.
@article{107987, author = {Michael E. Filippakis and Nikolaos S. Papageorgiou}, title = {Periodic solutions for differential inclusions in ${\Bbb R}^N$}, journal = {Archivum Mathematicum}, volume = {042}, year = {2006}, pages = {115-123}, zbl = {1164.34320}, mrnumber = {2240188}, language = {en}, url = {http://dml.mathdoc.fr/item/107987} }
Filippakis, Michael E.; Papageorgiou, Nikolaos S. Periodic solutions for differential inclusions in ${\Bbb R}^N$. Archivum Mathematicum, Tome 042 (2006) pp. 115-123. http://gdmltest.u-ga.fr/item/107987/
A topological fixed point theory for evolutions inclusions, Z. Anal. Anwendungen 20 (2001), 3–15. | MR 1826317
An averaging result for $l^1$-sequences and applications to weakly conditionally compact sets in $L^1(X)$, Israel J. Math. 32 (1979), 289–298. (1979) | MR 0571083
Existence of slow solutions for a class differential inclusions, J. Math. Anal. Appl. 96 (1983), 130–147. (1983) | MR 0717499
Topological degree and periodic solutions of differential inclusions, Nonlinear Anal. 37 (1999), 217–245. (1999) | MR 1689752 | Zbl 0936.34009
Nonconvex valued differential inclusions in Banach spaces, J. Math. Anal. Appl. 157 (1991), 469–494. (1991) | MR 1112329
Periodic solutions of functional differential inclusions and fixed points of $\gamma $-selectionable correspondences, J. Math. Anal. Appl. 96 (1983), 295–312. (1983) | MR 0719317
Existence and relaxation results for nonlinear second order multivalued boundary value problems in $\mathbb{R^N}$, J. Differential Equations 147 (1998), 123–154. (1998) | MR 1632661
Differential equations with discontinuous right hand side for planning procedures, J. Econom. Theory 4 (1972), 545–551. (1972) | MR 0449534
Periodic solutions for nonconvex differential inclusions, Proc. Amer. Math. Soc. 127 (1999), 89–94. (1999) | MR 1451808 | Zbl 0905.34036
On the existence of periodic solutions for nonconvex valued differential inclusions in $\mathbb{R^N}$, Proc. Amer. Math. Soc. 123 (1995), 3043–3050. (1995) | MR 1301503
Handbook of Multivalued Analysis. Volume I: Theory, Kluwer, Dordrecht, The Netherlands (1997). (1997) | MR 1485775 | Zbl 0887.47001
Handbook of Multivalued Analysis. Volume II: Applications, Kluwer, Dordrecht, The Netherlands (2000). | MR 1741926 | Zbl 0943.47037
On the existence of periodic solutions for differential inclusions, J. Math. Anal. Appl. 276 (2002), 168–183. | MR 1944344 | Zbl 1020.34015
The existence of periodic solutions to nonautonomous differential inclusions, Proc. Amer. Math. Soc. 104 (1988), 840–844. (1988) | MR 0931741 | Zbl 0692.34042
Periodic solutions of differential inclusions on compact subsets of $\mathbb{R^N}$, J. Math. Anal. Appl. 148 (1990), 202–212. (1990) | MR 1052055