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

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. Wa ewski and Schauder's fixed point theorem is used.