Abstract and Applied Analysis
Volume 3 (1998), Issue 3-4, Pages 363-375

On the existence of classical solutions for differential-functional IBVP

Krzysztof A. Topolski

Institut of Mathematics, University of Gdańsk, Wit Stwosz 57, Gdańsk 80-952, Poland

Received 25 July 1998

Copyright © 1998 Krzysztof A. Topolski. 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.


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.