On local attractivity and asymptotic stability of solutions of a quadratic Volterra integral equation
type: Item
instance of: scholarly article
title: On local attractivity and asymptotic stability of solutions of a quadratic Volterra integral equation
zbMATH Open document ID: 1175.45002
author: Józef Banaś
author: Beata Rzepka
published in: Applied Mathematics and Computation
publication date: 2009-07-01T00:00:00Z
review text: The authors study the integral equation \[ x(t) = p(t) +f(t, x(t))\int_0^t v(t, s, x(s))ds. \] They write the following: ``We will study the solvability of this equation in the space \(BC (\mathbb{R}_{+})\) consisting of all real functions defined, continuous and bounded on the interval \(\mathbb{R}_{+} = [0; \infty).\) More precisely, we will look for assumptions concerning the functions involved in this equation which guarantee that this equation has solution belonging to \(BC (\mathbb{R}_{+})\) and being locally attractive or asymptotic stable on \(\mathbb{R}_{+}\).'' As example the authors consider the equation \[ x(t) =t\exp(-2t) +\frac{1}{2\pi}\arctan(\sqrt{t} +tx(t)) \int_{0}^{t} \left( \frac{2x(s)^{2/3}+x(s)}{(s+1)(t^2+1)} +\frac{1}{10(t^2+1)} \right)\,ds . \]
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 47H30
Mathematics Subject Classification ID: 45M05
Mathematics Subject Classification ID: 45M10
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 5573823
zbMATH Keywords: quadratic Volterra integral equation
zbMATH Keywords: measure of noncompactness
zbMATH Keywords: uniform local attractivity
zbMATH Keywords: global attractivity
zbMATH Keywords: asymptotic stability
MaRDI profile type: Publication
full work available at URL: j.amc.2009.02.048
OpenAlex ID: W2030089065
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DOI: 10.1016/J.AMC.2009.02.048
description: scientific article; zbMATH DE number 5573823