The unique solution of boundary value problems for nonlinear second-order integral-differential equations of mixed type in Banach spaces
type: Item
instance of: scholarly article
title: The unique solution of boundary value problems for nonlinear second-order integral-differential equations of mixed type in Banach spaces
zbMATH Open document ID: 1156.34051
author: Zenggui Wang
author: Lishan Liu
author: Yonghong Wu
publication date: 2008-06-12T00:00:00Z
review text: Integral-differential equations of the form \[ -u''(t)=f(t,u(t),Tu(t),Su(t)),\qquad t\in[0,1] \] are considered, where \[ (Tu)(t)=\int_0^1 k(t,s)u(s)ds, \quad (Su)(t)=\int_0^1 h(t,s)u(s)ds \] with continuous \(h,k\), Banach space valued \(u\), Banach space valued \(f\). Under some order conditions, the existence of a unique solution is shown by an iteration process.
Mathematics Subject Classification ID: 34K10
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 5288029
zbMATH Keywords: integrodifferential equation
zbMATH Keywords: boundary value problem
zbMATH Keywords: ordered Banach space
reviewed by: András Bátkai
MaRDI profile type: Publication
full work available at URL: j.camwa.2007.04.018
OpenAlex ID: W2016335824
cites work: On the Existence of Positive Solutions of Ordinary Differential Equations
cites work: Multiple positive solutions of some boundary value problems
cites work: Positive solutions to second-order boundary value problems with sign-changing nonlinear terms
cites work: Extreme solutions of nonlinear, second order integro-differential equations in Banach spaces
cites work: Q3836448
cites work: Multiple solutions of two-point boundary value problems of ordinary differential equations in Banach spaces
cites work: Q4286040
cites work: Solvability of a third-order two-point boundary value problem
DOI: 10.1016/J.CAMWA.2007.04.018
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 5288029