Abstract and Applied Analysis
Volume 3 (1998), Issue 3-4, Pages 363-375
doi:10.1155/S1085337598000608

On the existence of classical solutions for differential-functional IBVP

Abstract

We consider the initial-boundary value problem for second order differential-functional equations of parabolic type. Functional dependence in the equation is of the Hale type. By using Leray-Schauder theorem we prove the existence of classical solutions. Our formulation and results cover a large class of parabolic problems both with a deviated argument and integro-differential equations.