Boundary Value Problems
Volume 2011 (2011), Article ID 965759, 10 pages
doi:10.1155/2011/965759
Research Article

Discontinuous Parabolic Problems with a Nonlocal Initial Condition

Abdelkader Boucherif

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

Received 28 February 2010; Revised 31 May 2010; Accepted 13 June 2010

Academic Editor: Feliz Manuel Minhós

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 study parabolic differential equations with a discontinuous nonlinearity and subjected to a nonlocal initial condition. We are concerned with the existence of solutions in the weak sense. Our technique is based on the Green's function, integral representation of solutions, the method of upper and lower solutions, and fixed point theorems for multivalued operators.