An existence result for a class of nonlinear functional integral equations

Abstract

We consider a general nonlinear functional integral equation, and we prove the existence of solutions of this equation in the space of Lebesgue integrable functions on $\R^+$. Our analysis uses a recent version of Krasnosel'skii's fixed point theorem (Theorem \ref{2t1}) and the concept of the measure of weak noncompactness. In the appendix, we give an extension of Theorem~\ref{2t1} to expansive mappings.