Advances in Difference Equations
Volume 2010 (2010), Article ID 143298, 8 pages
doi:10.1155/2010/143298
Research Article

On Connection between Second-Order Delay Differential Equations and Integrodifferential Equations with Delay

Leonid Berezansky,1 Josef Diblík,2,3 and Zdenĕk Šmarda3

1Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
2Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, 66237, Brno University of Technology, Brno, Czech Republic
3Department of Mathematics, Faculty of Electrical Engineering and Communication, 61600, Brno University of Technology, Brno, Czech Republic

Received 5 October 2009; Accepted 11 November 2009

Academic Editor: Ağacik Zafer

Copyright © 2010 Leonid Berezansky et al. 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.

Abstract

The existence and uniqueness of solutions and a representation of solution formulas are studied for the following initial value problem: x˙(t)+∫t0tK(t,s)x(h(s))ds=f(t),  t≥t0,  x∈ℝn, x(t)=φ(t), t<t0. Such problems are obtained by transforming second-order delay differential equations x¨(t)+a(t)x˙(g(t))+b(t)x(h(t))=0 to first-order differential equations.