Positive solutions of an infinite boundary value problem for \(n\)th-order nonlinear impulsive singular integro-differential equations in Banach spaces
type: Item
instance of: scholarly article
title: Positive solutions of an infinite boundary value problem for \(n\)th-order nonlinear impulsive singular integro-differential equations in Banach spaces
zbMATH Open document ID: 1257.45006
author: Yumei Xu
author: Haijun Zhang
published in: Applied Mathematics and Computation
publication date: 2012-06-18T00:00:00Z
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 47H08
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45G05
Mathematics Subject Classification ID: 45M20
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 45L05
zbMATH DE Number: 6047339
zbMATH Keywords: impulsive singular integro-differential equation
zbMATH Keywords: cone
zbMATH Keywords: positive solution
zbMATH Keywords: condensing operator
zbMATH Keywords: Mönch fixed point theorem
zbMATH Keywords: measure of noncompactness
zbMATH Keywords: ordered Banach space
zbMATH Keywords: method of successive approximation
MaRDI profile type: Publication
full work available at URL: j.amc.2011.11.100
OpenAlex ID: W2007521282
cites work: Q3042910
cites work: Q3995625
cites work: Q5632922
cites work: Q4853771
cites work: Positive solutions for \(n\)th-order nonlinear impulsive singular integro-differential equations on infinite intervals in Banach spaces
cites work: Positive solutions of an infinite boundary value problem for \(n\)th-order nonlinear impulsive singular integro-differential equations in Banach spaces
cites work: Existence of positive solutions for \(n\)th-order nonlinear impulsive singular integro-differential equations in Banach spaces
cites work: A class of \(n^{\text{th}}\)-order impulsive integrodifferential equations in Banach spaces.
cites work: Extremal solutions for \(n\)th-order impulsive integro-differential equations on the half-line in Banach spaces
cites work: Multiple positive solutions for \(n\)th-order impulsive integro-differential equations in Banach spaces
cites work: Existence of solutions for \(n\)th order impulsive integro-differential equations in a Banach space.
cites work: A class of second-order impulsive integro-differential equations on unbounded domain in a Banach space
cites work: Infinite boundary value problems for \(n\)th-order nonlinear impulsive integro-differential equations in Banach spaces
cites work: Q3421295
cites work: Method of upper and lower solutions for second-order impulsive integro-differential equations in a Banach space
cites work: Q4672620
cites work: Q3994493
cites work: Q4716265
cites work: Minimal nonnegative solutions for \(n\)th order integro-differential equations in Banach spaces
cites work: Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces
DOI: 10.1016/J.AMC.2011.11.100
review text: In an ordered Banach space \(E\), the existence of a positive (in the sense of the ordering) solution of the integro-differential equation NEWLINE\[NEWLINEx^{(n)}(t)=-f(t,x(t),x'(t),\ldots,x^{(n-1)},\int_0^tK(t,s)x(s)ds, \int_0^\infty H(t,s)x(s)ds)NEWLINE\]NEWLINE with jump conditions (for \(i=1,\ldots,n-1\) and \(k=1,2,\ldots\)) NEWLINE\[NEWLINEx^{(i)}(t_k^+)-x^{(i)}(t_k^-)=I_{ik}(x(t_k),\ldots,x^{(n-1)}(t_k))NEWLINE\]NEWLINE and boundary conditions with given \(x^{(i)}(0)\) \((i=1,\ldots,n-2)\) and \(x^{n-1}(\infty)\) is shown where the function \(f\) can have a singularity at \(t=0\). Also, it is shown that a certain method of successive approximation converges to the solution. The main tool for the existence result is an application of Mönch's fixed point theorem.
description: scientific article; zbMATH DE number 6047339