Existence Results on General Integrodifferential Evolution Equations in Banach Space

Abstract

In this paper we prove the existence of mild solutions of a general class of nonlinear evolution integrodifferential equation in Banach spaces. Based on the resolvent operator and the Schaefer fixed point theorem, a sufficient condition for the existence of general integrodifferential evolution equations is established.

Existence of Solutions for Nonlinear Neutral Integrodifferential Equations with Infinite Delay.

“…Pazy [8] used the method of semigroups to study the existence and uniqueness of mild, strong and classical solutions of semilinear evolution equation. In Sathiyanathan and Nandha [11] sufficient condition for the existence of mild solutions of a class of nonlinear evolution integrodifferential equation in Banach Spaces was proved using resolvent operator and Schaefer's fixed point theorem.…”