On Local Attractivity and Asymptotic Stability of Solutions of Nonlinear Volterra–Stieltjes Integral Equations in Two Variables

Abstract

In this paper we will study the existence of solutions depending on two variables of a nonlinear integral equation of Volterra–Stieltjes type in two variables, in the space of real functions which are continuous and bounded on the set ${\mathbb{R}}_{+}\times [0,M]$ . Moreover, we will give the characterization of those solutions. In our study we will utilize the Darbo type of fixed point theorem and apply a measure of noncompactness. In the last section we present particular cases of the considered equation.