Positive solutions of nonlinear singular boundary value problem in abstract space
type: Item
instance of: scholarly article
title: Positive solutions of nonlinear singular boundary value problem in abstract space
zbMATH Open document ID: 1070.34079
DOI: 10.1016/S0898-1221(04)90055-7
author: Yansheng Liu
author: Aiqin Qi
publication date: 2005-03-08T00:00:00Z
review text: The authors investigate the boundary value problem \[ x''(t)+f(t,x(t))=\theta, t\in (0,1),\quad x(0)=x(1)=\theta, \tag{P} \] in a Banach space \(E\), where \(f\) has singularities at \(t=0\), \(t=1\) and \(x=\theta\). Under suitable assumptions on \(f\), using the Mönch fixed-point theorem, the existence of a positive solution to (P) is proved. An example -- an infinite-dimensional singular differential system, is also presented.
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 34B18
zbMATH DE Number: 2142336
zbMATH Keywords: singular equation
zbMATH Keywords: boundary value problem
zbMATH Keywords: positive solution
zbMATH Keywords: fixed-point
zbMATH Keywords: Mönch fixed-point theorem
reviewed by: Rodica Luca
MaRDI profile type: Publication
cites work: Q4716265
cites work: Ordinary differential equations in Banach spaces
cites work: Q3904867
cites work: Positive solutions of semilinear differential equations with singularities
cites work: On the Existence of Positive Solutions of Ordinary Differential Equations
cites work: Second-order boundary value problems of singular type
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2142336