Local asymptotic attractivity for nonlinear quadratic functional integral equations
type: Item
instance of: scholarly article
title: Local asymptotic attractivity for nonlinear quadratic functional integral equations
zbMATH Open document ID: 1173.47056
author: Bapurao C. Dhage
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2009-02-19T00:00:00Z
review text: The paper deals with the quadratic functional-integral equation of mixed type \[ x(t)=[f(t,x(\alpha(t)))]\big(q(t)+\int_0^{\beta(t)}g(t,s,x(\gamma(s)))\,ds\big). \tag{1} \] Using a result about operator equations in Banach algebras, the author proves the existence of a solution of (1) in the space \(BC(\mathbb{R}_+,\mathbb{R})\). It is also proved that the solutions of (1) are uniformly locally asymptotically attractive on \(\mathbb{R}_+\).
reviewed by: Mirosława Zima
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 34K99
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 5509521
zbMATH Keywords: quadratic functional integral equation
zbMATH Keywords: fixed point theorem
zbMATH Keywords: uniformly locally asymptotically attractive solution
MaRDI profile type: Publication
full work available at URL: j.na.2008.02.109
OpenAlex ID: W2153041676
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DOI: 10.1016/J.NA.2008.02.109
description: scientific article; zbMATH DE number 5509521