The existence and compactness of the set of solutions for a nonlinear integrodifferential equation in N variables in a Banach space

Abstract

The paper is devoted to the study of a nonlinear integrodifferential equation in N variables with values in a general Banach space. By applying fixed point theorems in a suitable Banach space under appropriate conditions for subsets to be relatively compact, we prove the existence and the compactness of the set of solutions. In order to illustrate the results, we give two examples