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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 792431, 9 pages
http://dx.doi.org/10.1155/2013/792431
Research Article

Relaxation Problems Involving Second-Order Differential Inclusions

1Taibah University, Faculty of Applied Science, Department of Applied Mathematics, Al-Madinah, Saudi Arabia
2Mathematics Department, Faculty of Science, Helwan University, Cairo, Egypt

Received 12 November 2012; Accepted 12 March 2013

Academic Editor: Malisa R. Zizovic

Copyright © 2013 Adel Mahmoud Gomaa. 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

We present relaxation problems in control theory for the second-order differential inclusions, with four boundary conditions, a.e. on ; and, with boundary conditions, a.e. on , where , and is a multifunction from to the nonempty compact convex subsets of . We have results that improve earlier theorems.