Discontinuous Parabolic Problems with a Nonlocal Initial Condition
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:10.1155/2011/965759Published: 5 July 2010
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.