Measures of noncompactness in the study of asymptotically stable and ultimately nondecreasing solutions of integral equations
type: Item
instance of: scholarly article
title: Measures of noncompactness in the study of asymptotically stable and ultimately nondecreasing solutions of integral equations
zbMATH Open document ID: 1214.47044
DOI: 10.4171/ZAA/1408
author: Jürgen Appell
author: Józef Banaś
author: N. Merentes
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2010-08-16T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_abstract.php
review text: The authors introduce a new class of measures of noncompactness related to asymptotic stability and ultimate monotonicity in the space \(BC(\mathbb R)^+\). By using those measures of noncompactness and a fixed point theorem of Darbo type, they prove that the following functional integral equation \[ x(t)=m(t)+f(t,x(t))\int^t_0 g(t,\tau)h(\tau,x(\tau))\,d\tau,\quad t\geq 0, \] has at least one solution \(x\in BC(\mathbb R)^+\), which is nonnegative, asymptotically stable and ultimately nondecreasing. A concrete example is given to illustrate the abstract results.
Mathematics Subject Classification ID: 47H08
Mathematics Subject Classification ID: 26A48
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H30
zbMATH DE Number: 5770967
zbMATH Keywords: measure of noncompactness
zbMATH Keywords: Darbo fixed point theorem
zbMATH Keywords: superposition operator
zbMATH Keywords: quadratic functional integral equation
zbMATH Keywords: asymptotic stability
zbMATH Keywords: ultimate monotonicity
MaRDI profile type: Publication
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OpenAlex ID: W2050186169
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description: scientific article; zbMATH DE number 5770967