Electron. J. Diff. Eqns., Vol. 2005(2005), No. 50, pp. 1-10.

Existence of viable solutions for nonconvex differential inclusions

Messaoud Bounkhel, Tahar Haddad

Abstract:
We show the existence result of viable solutions to the differential inclusion
$$\displaylines{ \dot x(t)\in G(x(t))+F(t,x(t)) \cr x(t)\in S \quad \hbox{on } [0,T], }$$
where $F: [0,T]\times H\to H$ $(T>0)$ is a continuous set-valued mapping, $G:H\to H$ is a Hausdorff upper semi-continuous set-valued mapping such that $G(x)\subset \partial g(x)$, where $g :H\to \mathbb{R}$ is a regular and locally Lipschitz function and $S$ is a ball, compact subset in a separable Hilbert space $H$.

Submitted December 26, 2004. Published May 11, 2005.
Math Subject Classifications: 34A60, 34G25, 49J52, 49J53.
Key Words: Uniformly regular functions; normal cone; nonconvex differential inclusions.

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Messaoud Bounkhel
King Saud University, College of Science
Department of Mathematics
Riyadh 11451, Saudi Arabia
email: bounkhel@ksu.edu.sa
Tahar Haddad
University of Jijel
Department of Mathematics
B.P. 98, Ouled Aissa, Jijel, Algeria
email: haddadtr2000@yahoo.fr

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