ON THE EXISTENCE AND PROPERTIES OF SOLUTIONS FOR A 3-ORDER NONLINEAR INTEGRODIFFERENTIAL EQUATION IN THREE VARIABLES

Abstract

This paper is devoted to the study of existence, uniqueness and other properties of solutions of a 3-order nonlinear integrodifferential equation (IDE) in three variables in an arbitrary Banach space. The main tools employed in the analysis are based on the applications of fixed point theorems and a generalization of Ascoli-Arzela theorem. At first, we estab lish an appropriate Banach space for IDE and prove a sufficient condition for relatively compact subsets in this space. Next, by using Banach’s fixed point theorem, we consider the unique existence, stability and boundedness of the solution. Finally, by using Schauder’s fixed point theorem, we dis cuss the existence and compactness of the set of solutions. Furthermore, in order to verify the efficiency of the applied method, examples are given.