Monotonic solutions of a quadratic integral equation of Volterra type
type: Item
instance of: scholarly article
title: Monotonic solutions of a quadratic integral equation of Volterra type
zbMATH Open document ID: 1059.45002
DOI: 10.1016/S0898-1221(04)90024-7
author: Józef Banaś
author: Antonio Martinón
publication date: 2004-06-15T00:00:00Z
review text: The paper concerns the existence of nondecreasing solutions of the nonlinear quadratic Volterra integral equation of the form \[ x(t)=a(t)+x(t)\int_0^tv(t,\tau,x(\tau))d\tau, \quad t\in I=[0,T] \] in the space \(C(I)\) consisting of all real functions defined and continuous on the interval \(I\), where \(a(t)\) and \(v(t,\tau,x)\) are given while \(x=x(t)\) is an unknown function. The proof of the main result is based on the Darbo type fixed point theorem formulated in terms of axiomatic measures of noncompactness introduced by \textit{J. Banás} and \textit{K. Goebel} [Measures of noncompactness in Banach spaces, Lect. Notes Pure Appl. Math. 60 (1980; Zbl 0441.47056)]. The authors illustrate the main result and compare its assumptions by giving suitable interesting examples.
reviewed by: Dariusz Bugajewski
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 2075459
zbMATH Keywords: measure of noncompactness
zbMATH Keywords: monotonic solutions
zbMATH Keywords: Darbo type fixed point theorem
zbMATH Keywords: nondecreasing solutions
zbMATH Keywords: nonlinear quadratic Volterra integral equation
MaRDI profile type: Publication
cites work: Global existence for nonlinear operator inclusions
cites work: Q4253594
cites work: Q3997912
cites work: Q5185568
cites work: Existence principles for nonlinear resonant operator and integral equations
cites work: Q4045174
cites work: Quadratic equations and applications to Chandrasekhar's and related equations
cites work: Existence theorems for some quadratic integral equations
cites work: Q3263585
cites work: Existence theorems for an integral equation of the Chandrasekhar H- equation with perturbation
cites work: Existence and Uniqueness Theorems for the Neutron Transport Equation
cites work: Q5796557
cites work: Integral equations arising in the kinetic theory of gases
cites work: Solvability of Volterra-Stieltjes operator-integral equations and their applications
cites work: Q4937534
cites work: Q3883054
cites work: Punti uniti in trasformazioni a codominio non compatto
cites work: Q4329071
cites work: Q3913335
full work available at URL: s0898-1221(04)90024-7
OpenAlex ID: W2006434620
published in: Computers & Mathematics with Applications
Recommended article: Monotonic solutions of a class of quadratic integral equations of Volterra type
Recommended article: Monotonic solutions of a class of quadratic singular integral equations of Volterra type
Recommended article: The Existence of Monotonic Solutions of a Class of Quadratic Integral Equations of Volterra Type
Recommended article: On monotonic solutions of an integral equation of Volterra type
Recommended article: Existence of monotone solutions for a nonlinear quadratic integral equation of Volterra type
Recommended article: Monotonic solutions for quadratic integral equations
Recommended article: Q3349419
Recommended article: Monotone solutions of Volterra integral equations
Recommended article: Monotonic solutions of some singular integral equations of Volterra type
Recommended article: On monotonic solutions of an integral equation of Volterra–Stieltjes type
description: scientific article; zbMATH DE number 2075459