Previous |  Up |  Next

Article

Keywords:
lower semicontinuous multifunction; $C_M$-continuous selector; tangent cone; contingent derivative; Filippov regularization; fixed point
Summary:
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.
References:
[1] Aubin, J.-P.: A survey of viability theory. SIAM J. Control Optim. 28 (1990), 749-788. MR 1051623 | Zbl 0714.49021
[2] Aubin, J.-P., Cellina, A.: Differential Inclusions. Springer, Berlin, 1984. MR 0755330
[3] Bressan, A.: Directionally continuous selections and differential inclusions. Funkc. Ekvac. 31 (1988), 459-470. MR 0987798 | Zbl 0676.34014
[4] Haddad, G., Lasry, J.-M.: Periodic solutions of functional differential inclusions and fixed points of $\sigma $-selectionable correspondes. J. Math. Anal. Appl. 96 (1983), 295-312. MR 0719317
[5] Himmelberg, C., Van Vleck, F. S.: A note on solutions sets of differential inclusions. Rocky Mountain J. Math. 12 (1982), 621-625. MR 0683856
[6] Lasry, J.-M., Robert, R.: Degré topologique pour certains couples de fonctions et applications aux equations differentielles multivoques. C. R. Acad. Sci. Paris t. 283 (1976), 163-166. MR 0436196
[7] Macki, J., Nistri, P., Zecca, P.: The existence of periodic solutions to nonautonomous differential inclusions. Proc. Amer. Math. Soc. 104 (1988), 840-844. MR 0931741
[8] Michael, E.: Continuous selections I. Annals of Math. 63 (1956), 361-381. MR 0077107 | Zbl 0071.15902
[9] Moreau, J.-J.: Intersection of moving convex sets in a normed space. Math. Scand. 36 (1975), 159-173. MR 0442644 | Zbl 0311.54015
[10] Oxtoby, J.: Measure and Category. Springer, New York (1971). MR 0584443 | Zbl 0217.09201
[11] Papageorgiou, N. S.: On the attainable set of differential inclusions and control systems. J. Math. Anal. Appl. 125 (1987), 305-322. MR 0896170 | Zbl 0636.49018
[12] Papageorgiou, N. S.: Viable and periodic trajectories for differential inclusions in Banach spaces. Kobe Jour. Math. 5 (1988), 29-42. MR 0988577
[13] Papageorgiou, N. S.: On the existence of $\psi $-minimal viable solutions for a class of differential inclusions. Archivum Mathematicum (Brno) 27 (1991), 175-182. MR 1189213 | Zbl 0759.34014
Partner of
EuDML logo