Advances in Difference Equations
Volume 2011 (2011), Article ID 109570, 7 pages
doi:10.1155/2011/109570
Research Article

Nonlocal Conditions for Lower Semicontinuous Parabolic Inclusions

Abdelkader Boucherif

Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, P. O. Box 5046 Dhahran, 31261, Saudi Arabia

Received 4 December 2010; Accepted 11 February 2011

Academic Editor: John Graef

Copyright © 2011 Abdelkader Boucherif. 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 discuss conditions for the existence of at least one solution of a discontinuous parabolic equation with lower semicontinuous right hand side and a nonlocal initial condition of integral type. Our technique is based on fixed point theorems for multivalued maps.