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

Existence of viable solutions for nonconvex differential inclusions

Messaoud Bounkhel, Tahar Haddad

We show the existence result of viable solutions to the differential inclusion
 \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.

Show me the PDF file (229K), TEX file, and other files for this article.

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

Return to the EJDE web page