NOTE ON A VOLTERRA-FREDHOLM TYPE INTEGRODIFFERENTIAL EQUATION IN TWO VARIABLES

Abstract

In this note, we prove the existence and the compactness of the set of solutions for a Volterra-Fredholm type integrodifferential equation in two variables. The main tool is the fixed point theorem of Krasnosel’skii together with a necessary and sufficient condition for subsets to be relatively compact in an appropriate Banach space. An illustrative example is given.