Electron. J. Diff. Eqns., Vol. 2009(2009), No. 42, pp. 1-11.

Existence of mild solutions of a semilinear evolution differential inclusions with nonlocal conditions

Reem A. Al-Omair, Ahmed G. Ibrahim

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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