On Global Existence of Solutions for Abstract Nonlinear Functional Neutral Integro-Differential Equations with Nonlocal Condition

Rupali S. Jain, Machhindra B. Dhakne

Abstract

The aim of the present paper is to establish the global existence of solutions of initial value problem for nonlinear neutral functional integro-differential equations with nonlocal condition in Banach spaces. Our analysis is based on an application of the topological transversality theorem known as Leray-Schauder alternative, rely on a priori bounds of solution and the Pachpatte’s inequality.