A NONLINEAR VOLTERRA-HAMMERSTEIN INTEGRAL EQUATION IN THREE VARIABLES

Abstract

Motivated by recent known results about the solvability of nonlinear functionalintegral equations in one, two or n variables, this paper establishes the existence of asymp-totically stable solutions for a Volterra-Hammerstein integral equation in three variables.The proofs are completed via a fixed point theorem of Krasnosel'skii type, a condition forthe relative compactness of a subset in certain space and integral inequalities with explicit estimates.