Abstract and Applied Analysis
Volume 2004 (2004), Issue 4, Pages 337-345
doi:10.1155/S1085337504306020
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
Abstract
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), t∈I=[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.