Extremal solutions of a class of nonlinear integro-differential equations in Banach spaces

Abstract

The monotone iterative technique is applied to a class of nonlinear first order integro-differential equations in Banach spaces. First a linear system with a “small” nonlinear perturbation is solved using Banach’s Contraction Principle and the technique of Green’s function. Then based upon a comparison result, the existence of minimal and maximal solutions is proved.