Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 42, pp. 1-11.

Title: Existence of mild solutions of a semilinear evolution 
       differential inclusions with nonlocal conditions
   
Authors: Reem A. Al-Omair (King Faisal Univ., Jubail, Saudi Arabia)
         Ahmed G. Ibrahim (Cairo Univ.,  Egypt)

Abstract:
 In this paper we prove the existence of a mild solution for a semilinear
 evolution differential inclusion with nonlocal condition and governed by a
 family of linear operators, not necessarily bounded or closed, in a Banach
 space. No compactness assumption is assumed on the evolution operator
 generated by the family operators. Also, we prove that the set of mild
 solutions is compact.
 
Submitted January 1, 2009. Published March 24, 2009.
Math Subject Classifications: 34A60.
Key Words:  Evolution operator; generalized Cauchy operator; 
            measure of noncompactness; differential inclusions; 
	    nonlocal conditions; mild solutions.