Multiple positive solutions of a discrete difference system
type: Item
instance of: scholarly article
title: Multiple positive solutions of a discrete difference system
zbMATH Open document ID: 1030.39015
DOI: 10.1016/S0096-3003(02)00354-5
author: Jian-Ping Sun
author: Wan-Tong Li
published in: Applied Mathematics and Computation
publication date: 2003-07-30T00:00:00Z
review text: The authors study the discrete system \[ \Delta^2u_1(k)+f_1(k,u_1(k),u_2(k))=0,\quad \Delta^2u_2(k)+f_2(k,u_1(k),u_2(k))=0, \] \(k\in[0,T]\), with the Dirichlet boundary conditions \[ u_1(0)=u_1(T+2)=0,\quad u_2(0)=u_2(T+2)=0. \] Sufficient conditions for existence of at least three positive solutions to the above boundary value problem are given. The proof is based on the fixed point theorem of \textit{R. W. Leggett} and \textit{L. R. Williams} [Indiana Univ. Math. J. 28, 673-688 (1979; Zbl 0421.47033)].
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A12
zbMATH DE Number: 1957187
zbMATH Keywords: multiple positive solutions
zbMATH Keywords: discrete difference system
zbMATH Keywords: boundary value problem
zbMATH Keywords: cone
zbMATH Keywords: fixed point
reviewed by: Pavel Rehak
MaRDI profile type: Publication
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full work available at URL: s0096-3003(02)00354-5
OpenAlex ID: W2121227675
description: scientific article; zbMATH DE number 1957187