Geodesic
On the existence of periodic solutions for nonconvex differential inclusions
Archivum mathematicum, Tome 32 (1996) no. 1, pp. 1-8 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 34A60, 34G20
Keywords: lower semicontinuous multifunction; $C_M$-continuous selector; tangent cone; contingent derivative; Filippov regularization; fixed point 
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Kravvaritis, Dimitrios; Papageorgiou, Nikolaos S. On the existence of periodic solutions for nonconvex differential inclusions. Archivum mathematicum, Tome 32 (1996) no. 1, pp. 1-8. http://geodesic.mathdoc.fr/item/ARM_1996_32_1_a0/

[1] Aubin, J.-P.: A survey of viability theory. SIAM J. Control Optim. 28 (1990), 749-788. | MR | Zbl

[2] Aubin, J.-P., Cellina, A.: Differential Inclusions. Springer, Berlin, 1984. | MR

[3] Bressan, A.: Directionally continuous selections and differential inclusions. Funkc. Ekvac. 31 (1988), 459-470. | MR | Zbl

[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

[5] Himmelberg, C., Van Vleck, F. S.: A note on solutions sets of differential inclusions. Rocky Mountain J. Math. 12 (1982), 621-625. | MR

[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

[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

[8] Michael, E.: Continuous selections I. Annals of Math. 63 (1956), 361-381. | MR | Zbl

[9] Moreau, J.-J.: Intersection of moving convex sets in a normed space. Math. Scand. 36 (1975), 159-173. | MR | Zbl

[10] Oxtoby, J.: Measure and Category. Springer, New York (1971). | MR | Zbl

[11] Papageorgiou, N. S.: On the attainable set of differential inclusions and control systems. J. Math. Anal. Appl. 125 (1987), 305-322. | MR | Zbl

[12] Papageorgiou, N. S.: Viable and periodic trajectories for differential inclusions in Banach spaces. Kobe Jour. Math. 5 (1988), 29-42. | MR

[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 | Zbl