Krasnoselskii’s unification, Volterra’s integrodifferential equation, and the method of Aizerman

Abstract

In this paper we continue the study of an idea of Krasnoselskii for a unifying theory of differential equations of many types based on a certain kind of inversion of the perturbed differential
operator and a fixed point theorem. Earlier we had studied the idea for fractional differential equations, neutral differential equations, and for a linear form of an integrodifferential equation studied by Volterra. Here, we continue that study of Volterra’s problem for nonlinear equations based on the
global linearization technique of Aizerman.