Existence of positive solutions of BVPs for third-order discrete nonlinear difference systems
type: Item
instance of: scholarly article
title: Existence of positive solutions of BVPs for third-order discrete nonlinear difference systems
zbMATH Open document ID: 1073.39005
published in: Applied Mathematics and Computation
publication date: 2004-11-23T00:00:00Z
review text: The following boundary value problem is considered \[ \begin{gathered} \Delta^3 u_1(k)+ f_1(k, u_1(k), u_2(k))= 0,\quad k\in [0,T],\\ \Delta^3 u_2(k)+ f_2(k, u_1(k), u_2(k))= 0,\quad k\in [0,T],\\ u_1(0)= u_1(1)= u_1(T+ 3)= 0= u_2(0)= u_2(T+ 3).\end{gathered} \] New results of the existence, nonexistence and multiplicity are obtained using Krasnosel'skij's fixed point theorem in a cone. In particular, it is proved that the above boundary value problem has \(N\) positive solutions under suitable conditions, where \(N\) is an arbitrary, positive integer.
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 2117977
zbMATH Keywords: positive solution
zbMATH Keywords: cone
zbMATH Keywords: boundary value problem
zbMATH Keywords: Krasnosel'skij's fixed point theorem
author: Wan-Tong Li
author: Jian-Ping Sun
reviewed by: Stefan Balint
MaRDI profile type: Publication
full work available at URL: j.amc.2003.06.017
OpenAlex ID: W2023339959
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DOI: 10.1016/J.AMC.2003.06.017
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description: scientific article; zbMATH DE number 2117977