On the solution of Volterra integral equations with decomposable kernel functions

Abstract

We consider the solution of a class of nonlinear Volterra integral equations, x(t)=g(t)+∫⁡t0tk(t,s;x(s))ds, where t≥t0 and the kernel function k is finitely decomposable, and derive variation of parameters formulae that provide the solution of corresponding perturbed nonlinear equations. We attain this by relating the integral equations to a certain class of initial value problems for ODEs, for which variation of parameters are also formulated.