On nonlinear integrodifferential equations in two variables

Abstract

This paper is devoted to the study of existence results and some properties of solutions of m-order nonlinear integrodifferential equations in two variables. The main tools are the Banach fixed point theorem or Schauder fixed point theorem coupled with the definitions of suitable Banach spaces and adding appropriate conditions which are useful to yield relatively compact subsets in these space. To our knowledge, these techniques have not been used before. In order to illustrate the results obtained here, two examples are given.