Existence of positive solutions of boundary value problem for a discrete difference system
type: Item
instance of: scholarly article
title: Existence of positive solutions of boundary value problem for a discrete difference system
zbMATH Open document ID: 1064.39013
published in: Applied Mathematics and Computation
publication date: 2004-11-23T00:00:00Z
review text: The authors study the discrete system \(\Delta^2u_i(k)+f_i(k,u_1(k),u_2(k))=0\) with the Dirichlet boundary conditions \(u_i(0)=u_i(T+2)=0\), where \(i=1,2\), \(T>1\) is a fixed integer, \(k\in\{0,1,2,\dots,T\}\), \(\Delta u(k)=u(k+1)-u(k)\), \(\Delta^2 u(k)=\Delta(\Delta u(k))\). In their recent paper, the authors [ibid. 143, No. 2--3, 213--221 (2003; Zbl 1030.39015)] obtained some sufficient conditions for the existence of three positive (that is, nonnegative and nontrivial) solutions of the above system by using the Leggett-Williams fixed point theorem. In the paper under review, they continue their investigation of this system and prove some sufficient conditions for the existence of one or two positive solutions. In this case the proof is based on a nonlinear alternative of Leray-Schauder type and the Krasnoselskii fixed point theorem on a cone.
reviewed by: Oleksiy Karlovych
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A12
zbMATH DE Number: 2118014
zbMATH Keywords: discrete system
zbMATH Keywords: positive solution
zbMATH Keywords: cone
zbMATH Keywords: nonlinear alternative of Leray-Schauder type
zbMATH Keywords: Krasnoselskii fixed point theorem
author: Jian-Ping Sun
author: Wan-Tong Li
MaRDI profile type: Publication
full work available at URL: j.amc.2003.06.014
OpenAlex ID: W1996771249
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DOI: 10.1016/J.AMC.2003.06.014
description: scientific article; zbMATH DE number 2118014