Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 50, pp. 1-10.
Title: Existence of viable solutions for nonconvex
differential inclusions
Authors: Messaoud Bounkhel (King Saud Univ., Saudi Arabia)
Tahar Haddad (Univ. of Jijel, Algeria)
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.