Multiple Positive Solutions of a Second Order Nonlinear Semipositone m-Point Boundary Value Problem on Time Scales

Multiple Positive Solutions of a Second Order Nonlinear Semipositone m-Point Boundary Value Problem on Time Scales

In this paper, we study a general second-order m-point boundary value problem for nonlinear singular dynamic equation on time scales uΔ∇(t)+a(t)uΔ(t)+b(t)u(t)+λq(t)f(t,u(t))=0, t∈(0,1)𝕋, u(ρ(0))=0, u(σ(1))=∑i=1m-2αiu(ηi). This paper shows the existence of multiple positive solutions if f...

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Main Authors: Chengjun Yuan, Yongming Liu
Format: Article
Language:English
Published: Hindawi Limited 2010-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2010/261741
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spelling doaj-e8d10dc5f1c54e09869cc5506639b8372020-11-24T20:44:15ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/261741261741Multiple Positive Solutions of a Second Order Nonlinear Semipositone m-Point Boundary Value Problem on Time ScalesChengjun Yuan0Yongming Liu1Department of Mathematics, East China Normal University, Shanghai 200241, ChinaDepartment of Mathematics, East China Normal University, Shanghai 200241, ChinaIn this paper, we study a general second-order m-point boundary value problem for nonlinear singular dynamic equation on time scales uΔ∇(t)+a(t)uΔ(t)+b(t)u(t)+λq(t)f(t,u(t))=0, t∈(0,1)𝕋, u(ρ(0))=0, u(σ(1))=∑i=1m-2αiu(ηi). This paper shows the existence of multiple positive solutions if f is semipositone and superlinear. The arguments are based upon fixed-point theorems in a cone.http://dx.doi.org/10.1155/2010/261741
collection DOAJ
language English
format Article
sources DOAJ
author Chengjun Yuan
Yongming Liu
spellingShingle Chengjun Yuan
Yongming Liu
Multiple Positive Solutions of a Second Order Nonlinear Semipositone m-Point Boundary Value Problem on Time Scales
Abstract and Applied Analysis
author_facet Chengjun Yuan
Yongming Liu
author_sort Chengjun Yuan
title Multiple Positive Solutions of a Second Order Nonlinear Semipositone m-Point Boundary Value Problem on Time Scales
title_short Multiple Positive Solutions of a Second Order Nonlinear Semipositone m-Point Boundary Value Problem on Time Scales
title_full Multiple Positive Solutions of a Second Order Nonlinear Semipositone m-Point Boundary Value Problem on Time Scales
title_fullStr Multiple Positive Solutions of a Second Order Nonlinear Semipositone m-Point Boundary Value Problem on Time Scales
title_full_unstemmed Multiple Positive Solutions of a Second Order Nonlinear Semipositone m-Point Boundary Value Problem on Time Scales
title_sort multiple positive solutions of a second order nonlinear semipositone m-point boundary value problem on time scales
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2010-01-01
description In this paper, we study a general second-order m-point boundary value problem for nonlinear singular dynamic equation on time scales uΔ∇(t)+a(t)uΔ(t)+b(t)u(t)+λq(t)f(t,u(t))=0, t∈(0,1)𝕋, u(ρ(0))=0, u(σ(1))=∑i=1m-2αiu(ηi). This paper shows the existence of multiple positive solutions if f is semipositone and superlinear. The arguments are based upon fixed-point theorems in a cone.
url http://dx.doi.org/10.1155/2010/261741
work_keys_str_mv AT chengjunyuan multiplepositivesolutionsofasecondordernonlinearsemipositonempointboundaryvalueproblemontimescales
AT yongmingliu multiplepositivesolutionsofasecondordernonlinearsemipositonempointboundaryvalueproblemontimescales
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