Reem A. Al-Omair, Ahmed G. Ibrahim
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.
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Reem A. Al-Omair King Faisal University, Collage of Education in Jubail Mathematics Department, Jubail, Saudi Arabia email: omair-reem@hotmail.com | |
Ahmed G. Ibrahim Cairo University, Faculty of Science Mathematics Department, Egypt email: agamal2000@yahoo.com |
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