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.