Existence of mild solutions of second order evolution integro-differential equations in the Fre'chet spaces

Abstract

In this article, we shall establish sufficient conditions for the existence of mild solutions for second order semilinear integro-differential evolution equations in Fre'chet spaces $C(mathbb{R}_+ , E)$, where $E$ is an Banach space. Our approach is based on the concept of a measure of noncompactness and Tykhonoff fixed point theorem. For illustration we give an example.