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

Document Type: Research Paper

Author

Department of Mathematics, Bizerte Preparatory Engineering Institute, Tunisia

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.

Keywords