Open Access Research Article

Discontinuous Parabolic Problems with a Nonlocal Initial Condition

Abdelkader Boucherif

Author Affiliations

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

Boundary Value Problems 2011, 2011:965759  doi:10.1155/2011/965759

Published: 5 July 2010

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.