Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 14, pp. 1-8.

Title: Existence of solutions to a paratingent equation with delayed argument

Author: Lotfi Boudjenah (Univ. d'Oran, Algeria)

Abstract: 
 In this work we prove the existence of solutions of a  class of 
 paratingent equations with delayed argument,  
 $$
 (Pt\;x)(t)\subset F([x]_{t})\quad\hbox{for } t\geq 0  
 $$
 with the initial condition $x(t)=\xi (t)$ for $t\leq 0$.  
 We use a fixed  point theorem to obtain a solution and then  
 provide an estimate for the solution.
 
Submitted December 6, 2004. Published January 30, 2005.
Math Subject Classifications: 34A60, 49J24, 49K24.
Key Words: Convex delayed argument; differential inclusion; paratingent;
           set-valued function; upper semi-continuity.