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.

Abstract

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.