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The Scientific World Journal
Volume 2013, Article ID 591620, 7 pages
http://dx.doi.org/10.1155/2013/591620
Research Article

Existence Results for Differential Inclusions with Nonlinear Growth Conditions in Banach Spaces

Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received 24 September 2013; Accepted 4 November 2013

Academic Editors: N. Henderson, Z. Mukandavire, and X. Song

Copyright © 2013 Messaoud Bounkhel. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In the Banach space setting, the existence of viable solutions for differential inclusions with nonlinear growth; that is, a.e. on , , , , (*), where is a closed subset in a Banach space , , , , is an upper semicontinuous set-valued mapping with convex values satisfying , , where , with , and . The existence of solutions for nonconvex sweeping processes with perturbations with nonlinear growth is also proved in separable Hilbert spaces.