Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (280 KB) | Metadata | Table of Contents | ZAA summary
Online access to the full text of Zeitschrift für Analysis und ihre Anwendungen is restricted to the subscribers of the journal, who are encouraged to communicate their IP-address(es) to their agent or directly to the publisher at
subscriptions@ems-ph.org
Volume 36, Issue 1, 2017, pp. 79–98
DOI: 10.4171/ZAA/1580

Published online: 2017-01-06

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

Beata Rzepka[1]

(1) Rzeszów University of Technology, Poland

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.

Keywords: Nonlinear Volterra–Stieltjes integral equation, fixed point theorem, measure of noncompactness, uniform local attractivity, asymptotic stability

Rzepka Beata: On Local Attractivity and Asymptotic Stability of Solutions of Nonlinear Volterra–Stieltjes Integral Equations in Two Variables. Z. Anal. Anwend. 36 (2017), 79-98. doi: 10.4171/ZAA/1580