Solvability of a system of integral equations of Volterra type in the Fr$\acute{e}$chet space $L^p_{loc}(\Bbb{R}_+)$ via measure of noncompactness

Abstract

The purpose of this article is to analyze the existence of solutions for a system of integral equations of Volterra type in the Fr$\acute{e}$chet space $L^p_{loc}(\Bbb{R}_+)$ and prove a fixed point theorem of Darbo-type in this space.
The technique of measure of noncompactness by applying fixed point theorem is the main tool in carrying out our proof. Moreover, we present an example to show the efficiency of our results.