Advances in Difference Equations
Volume 2010 (2010), Article ID 810453, 13 pages
Research Article

Singular Cauchy Initial Value Problem for Certain Classes of Integro-Differential Equations

Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, 616 00 Brno, Czech Republic

Received 30 December 2009; Accepted 10 March 2010

Academic Editor: Ağacik Zafer

Copyright © 2010 Zdeněk Šmarda. 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 existence and uniqueness of solutions and asymptotic estimate of solution formulas are studied for the following initial value problem: g(t)y(t)=ay(t)[1+f(t,y(t),0+tK(t,s,y(t),y(s))ds)], y(0+)=0, t(0,t0], where a>0 is a constant and t0>0. An approach which combines topological method of T. Ważewski and Schauder's fixed point theorem is used.