Abstract and Applied Analysis
Volume 2004 (2004), Issue 4, Pages 337-345

Linear differential equations with unbounded delays and a forcing term

Jan Čermák and Petr Kundrát

Institute of Mathematics, Brno University of Technology, Technická 2, Brno 61669, Czech Republic

Received 10 September 2002

Copyright © 2004 Jan Čermák and Petr Kundrát. 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.


The paper discusses the asymptotic behaviour of all solutions of the differential equation y˙(t)=a(t)y(t)+i=1nbi(t)y(τi(t))+f(t), tI=[t0,), with a positive continuous function a, continuous functions bi, f, and n continuously differentiable unbounded lags. We establish conditions under which any solution y of this equation can be estimated by means of a solution of an auxiliary functional equation with one unbounded lag. Moreover, some related questions concerning functional equations are discussed as well.