Three positive fixed points of nonlinear operators on ordered Banach spaces
type: Item
instance of: scholarly article
title: Three positive fixed points of nonlinear operators on ordered Banach spaces
zbMATH Open document ID: 1005.47051
DOI: 10.1016/S0898-1221(01)00156-0
publication date: 2002-06-13T00:00:00Z
review text: The authors generalize the triple fixed-point theorem of Leggett and Williams, which is a theorem giving conditions that imply the existence of three fixed points of an operator defined on a cone in a Banach space. As an application of the abstract result, the authors prove the existence of three positive symmetric solutions of the discrete second-order nonlinear conjugate boundary value problem \[ \Delta^2 x(t-1)+f(x(t))=0, \text{for all} t\in [a+1,b+1], \] \[ x(a)=0=x(b+2), \] where \(f: \mathbb R\to \mathbb R\) is continuous and \(f\) is nonnegative for \(x\geq 0.\)
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 39A05
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 65Q05
zbMATH DE Number: 1755253
zbMATH Keywords: fixed point theorems
zbMATH Keywords: difference equations
zbMATH Keywords: positive solutions
zbMATH Keywords: boundary
zbMATH Keywords: positive symmetric solutions
zbMATH Keywords: discrete second-order nonlinear conjugate boundary value problem
author: Richard I. Avery
author: Allan Peterson
reviewed by: Sotiris K. Ntouyas
MaRDI profile type: Publication
cites work: Q4271322
cites work: Q4253594
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cites work: Three symmetric positive solutions for a second-order boundary value problem
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cites work: Multiple symmetric positive solutions for a second order boundary value problem
full work available at URL: s0898-1221(01)00156-0
OpenAlex ID: W2079893790
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1755253