Using a Nagumo type tangential condition and a recent theorem on the existence of directionally continuous selector for a lower semicontinuous multifunctions, we establish the existence of periodic trajectories for nonconvex differential inclusions.
@article{107557,
author = {Dimitrios Kravvaritis and Nikolaos S. Papageorgiou},
title = {On the existence of periodic solutions for nonconvex differential inclusions},
journal = {Archivum Mathematicum},
volume = {032},
year = {1996},
pages = {1-8},
zbl = {0870.34018},
mrnumber = {1399836},
language = {en},
url = {http://dml.mathdoc.fr/item/107557}
}
Kravvaritis, Dimitrios; Papageorgiou, Nikolaos S. On the existence of periodic solutions for nonconvex differential inclusions. Archivum Mathematicum, Tome 032 (1996) pp. 1-8. http://gdmltest.u-ga.fr/item/107557/
A survey of viability theory, SIAM J. Control Optim. 28 (1990), 749-788. (1990) | MR 1051623 | Zbl 0714.49021
Differential Inclusions, Springer, Berlin, 1984. (1984) | MR 0755330
Directionally continuous selections and differential inclusions, Funkc. Ekvac. 31 (1988), 459-470. (1988) | MR 0987798 | Zbl 0676.34014
Periodic solutions of functional differential inclusions and fixed points of $\sigma $-selectionable correspondes, J. Math. Anal. Appl. 96 (1983), 295-312. (1983) | MR 0719317
A note on solutions sets of differential inclusions, Rocky Mountain J. Math. 12 (1982), 621-625. (1982) | MR 0683856
Degré topologique pour certains couples de fonctions et applications aux equations differentielles multivoques, C. R. Acad. Sci. Paris t. 283 (1976), 163-166. (1976) | MR 0436196
The existence of periodic solutions to nonautonomous differential inclusions, Proc. Amer. Math. Soc. 104 (1988), 840-844. (1988) | MR 0931741
Continuous selections I, Annals of Math. 63 (1956), 361-381. (1956) | MR 0077107 | Zbl 0071.15902
Intersection of moving convex sets in a normed space, Math. Scand. 36 (1975), 159-173. (1975) | MR 0442644 | Zbl 0311.54015
Measure and Category, Springer, New York (1971). (1971) | MR 0584443 | Zbl 0217.09201
On the attainable set of differential inclusions and control systems, J. Math. Anal. Appl. 125 (1987), 305-322. (1987) | MR 0896170 | Zbl 0636.49018
Viable and periodic trajectories for differential inclusions in Banach spaces, Kobe Jour. Math. 5 (1988), 29-42. (1988) | MR 0988577
On the existence of $\psi $-minimal viable solutions for a class of differential inclusions, Archivum Mathematicum (Brno) 27 (1991), 175-182. (1991) | MR 1189213 | Zbl 0759.34014