ON A NONLINEAR INTEGRODIFFERENTIAL EQUATION IN TWO VARIABLES WITH VALUES IN A GENERAL BANACH SPACE

Abstract

The paper is devoted to the study of a nonlinear integrodifferential equation in two variables with values in a general Banach space. Applying the fixed point theorems together with the definition of a suitable Banach space and the establishment of appro- priate conditions for subsets to be relatively compact in this space, the existence and the compactness of the set of solutions are proved. Two illustrative examples are given.