Existence and Multiplicity of Positive Solutions of a Nonlinear Discrete Fourth-Order Boundary Value Problem

Existence and Multiplicity of Positive Solutions of a Nonlinear Discrete Fourth-Order Boundary Value Problem

we show the existence and multiplicity of positive solutions of the nonlinear discrete fourth-order boundary value problem Δ4ut-2=λhtfut, t∈T2, u1=uT+1=Δ2u0=Δ2uT=0, where λ>0, h:T2→(0,∞) is continuous, and f:R→[0,∞) is continuous, T>4, T2=2,3,…,T. The main tool is the Dancer's global bifu...

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Main Authors: Ruyun Ma, Yanqiong Lu
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/918082
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spelling doaj-8b34e621413741b8a7281701b70d05ae2020-11-24T23:21:17ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/918082918082Existence and Multiplicity of Positive Solutions of a Nonlinear Discrete Fourth-Order Boundary Value ProblemRuyun Ma0Yanqiong Lu1Department of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaDepartment of Mathematics, Northwest Normal University, Lanzhou 730070, Chinawe show the existence and multiplicity of positive solutions of the nonlinear discrete fourth-order boundary value problem Δ4ut-2=λhtfut, t∈T2, u1=uT+1=Δ2u0=Δ2uT=0, where λ>0, h:T2→(0,∞) is continuous, and f:R→[0,∞) is continuous, T>4, T2=2,3,…,T. The main tool is the Dancer's global bifurcation theorem.http://dx.doi.org/10.1155/2012/918082
collection DOAJ
language English
format Article
sources DOAJ
author Ruyun Ma
Yanqiong Lu
spellingShingle Ruyun Ma
Yanqiong Lu
Existence and Multiplicity of Positive Solutions of a Nonlinear Discrete Fourth-Order Boundary Value Problem
Abstract and Applied Analysis
author_facet Ruyun Ma
Yanqiong Lu
author_sort Ruyun Ma
title Existence and Multiplicity of Positive Solutions of a Nonlinear Discrete Fourth-Order Boundary Value Problem
title_short Existence and Multiplicity of Positive Solutions of a Nonlinear Discrete Fourth-Order Boundary Value Problem
title_full Existence and Multiplicity of Positive Solutions of a Nonlinear Discrete Fourth-Order Boundary Value Problem
title_fullStr Existence and Multiplicity of Positive Solutions of a Nonlinear Discrete Fourth-Order Boundary Value Problem
title_full_unstemmed Existence and Multiplicity of Positive Solutions of a Nonlinear Discrete Fourth-Order Boundary Value Problem
title_sort existence and multiplicity of positive solutions of a nonlinear discrete fourth-order boundary value problem
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2012-01-01
description we show the existence and multiplicity of positive solutions of the nonlinear discrete fourth-order boundary value problem Δ4ut-2=λhtfut, t∈T2, u1=uT+1=Δ2u0=Δ2uT=0, where λ>0, h:T2→(0,∞) is continuous, and f:R→[0,∞) is continuous, T>4, T2=2,3,…,T. The main tool is the Dancer's global bifurcation theorem.
url http://dx.doi.org/10.1155/2012/918082
work_keys_str_mv AT ruyunma existenceandmultiplicityofpositivesolutionsofanonlineardiscretefourthorderboundaryvalueproblem
AT yanqionglu existenceandmultiplicityofpositivesolutionsofanonlineardiscretefourthorderboundaryvalueproblem
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