On Solvability of the Integro-Differential Equations

Abstract

In this paper, we study the existence of solution to integro-differential equations in the space of Lebesgue-integrable  on un-bounded interval after transformed to nonlinear integral functional equation, the used tool is the fixed point theorem due to Schauder with weak measure of non compactness, due to De-Blasi. In addition, we give an example which satisfies the conditions of our existence theorem.