Twin solutions to singular semipositone problems.
type: Item
instance of: scholarly article
title: Twin solutions to singular semipositone problems.
zbMATH Open document ID: 1043.34021
DOI: 10.1016/S0022-247X(03)00478-5
author: Yansheng Liu
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-11-16T00:00:00Z
review text: The author investigates the existence of multiple positive solutions to the following singular semipositone problem: \[ y''+\lambda f(t,y)=0,\quad t\in(0,1),\quad y(0)=y(1)=0, \tag{1\(_\lambda\)} \] where \(\lambda>0\), and \(f(t,y)\) has not necessarily a constant sign and may be singular at \(t=0\), \(t=1\) and \(y=0\). More precisely, it is shown that, if appropriate assumptions hold on \(f\), then for any \(r>0\) there exists \(\bar\lambda>0\) such that, for any \(\lambda\in (0,\bar\lambda)\), (1\(_\lambda\)) has at least two positive solutions \(x\) and \(y\) satisfying \(0<\| x\| <r<\| y\| \). The proof is based upon a fixed-point index argument.
reviewed by: Marco Spadini
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 34B18
zbMATH DE Number: 2003904
zbMATH Keywords: multiple positive solutions
zbMATH Keywords: singular semipositone problem
zbMATH Keywords: fixed point index
MaRDI profile type: Publication
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cites work: Boundary-irregular solutions to singular boundary value problems
description: scientific article; zbMATH DE number 2003904