Abstract and Applied Analysis
Volume 2012 (2012), Article ID 918281, 18 pages
http://dx.doi.org/10.1155/2012/918281
Research Article

Singular Initial Value Problem for a System of Integro-Differential Equations

Zdeněk Šmarda1 and Yasir Khan2

1Department of Mathematics, Brno University of Technology, 61600 Brno, Czech Republic
2Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Received 29 October 2012; Accepted 15 November 2012

Academic Editor: Juntao Sun

Copyright © 2012 Zdeněk Šmarda and Yasir Khan. 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

Analytical properties like existence, uniqueness, and asymptotic behavior of solutions are studied for the following singular initial value problem: ,   ,   , where ,   ,   are constants and . An approach which combines topological method of T. Ważewski and Schauder's fixed point theorem is used. Particular attention is paid to construction of asymptotic expansions of solutions for certain classes of systems of integrodifferential equations in a right-hand neighbourhood of a singular point.