Triple Positive Solutions for Third-Order m-Point Boundary Value Problems on Time Scales

Triple Positive Solutions for Third-Order m-Point Boundary Value Problems on Time Scales

We study the following third-order m-point boundary value problems on time scales (φ(uΔ∇))∇+a(t)f(u(t))=0, t∈[0,T]T, u(0)=∑i=1m−2biu(ξi), uΔ(T)=0, φ(uΔ∇(0))=∑i=1m−2ciφ(uΔ∇(ξi)), where φ:R→R is an increasing homeomorphism and homomorphism and φ(0)=0, 0<ξ1<⋯<ξm−2<ρ(T). We obtain the e...

Full description

Bibliographic Details
Main Authors: Jian Liu, Fuyi Xu
Format: Article
Language:English
Published: Hindawi Limited 2009-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2009/123283
id doaj-f32b5f1ca7db41fea92f8ed3595485a5
record_format Article
spelling doaj-f32b5f1ca7db41fea92f8ed3595485a52020-11-24T21:09:29ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2009-01-01200910.1155/2009/123283123283Triple Positive Solutions for Third-Order m-Point Boundary Value Problems on Time ScalesJian Liu0Fuyi Xu1School of Statistics and Mathematics Science, Shandong Economics University, Jinan, Shandong 250014, ChinaSchool of Science, Shandong University of Technology, Zibo, Shandong 255049, ChinaWe study the following third-order m-point boundary value problems on time scales (φ(uΔ∇))∇+a(t)f(u(t))=0, t∈[0,T]T, u(0)=∑i=1m−2biu(ξi), uΔ(T)=0, φ(uΔ∇(0))=∑i=1m−2ciφ(uΔ∇(ξi)), where φ:R→R is an increasing homeomorphism and homomorphism and φ(0)=0, 0<ξ1<⋯<ξm−2<ρ(T). We obtain the existence of three positive solutions by using fixed-point theorem in cones. The conclusions in this paper essentially extend and improve the known results.http://dx.doi.org/10.1155/2009/123283
collection DOAJ
language English
format Article
sources DOAJ
author Jian Liu
Fuyi Xu
spellingShingle Jian Liu
Fuyi Xu
Triple Positive Solutions for Third-Order m-Point Boundary Value Problems on Time Scales
Discrete Dynamics in Nature and Society
author_facet Jian Liu
Fuyi Xu
author_sort Jian Liu
title Triple Positive Solutions for Third-Order m-Point Boundary Value Problems on Time Scales
title_short Triple Positive Solutions for Third-Order m-Point Boundary Value Problems on Time Scales
title_full Triple Positive Solutions for Third-Order m-Point Boundary Value Problems on Time Scales
title_fullStr Triple Positive Solutions for Third-Order m-Point Boundary Value Problems on Time Scales
title_full_unstemmed Triple Positive Solutions for Third-Order m-Point Boundary Value Problems on Time Scales
title_sort triple positive solutions for third-order m-point boundary value problems on time scales
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2009-01-01
description We study the following third-order m-point boundary value problems on time scales (φ(uΔ∇))∇+a(t)f(u(t))=0, t∈[0,T]T, u(0)=∑i=1m−2biu(ξi), uΔ(T)=0, φ(uΔ∇(0))=∑i=1m−2ciφ(uΔ∇(ξi)), where φ:R→R is an increasing homeomorphism and homomorphism and φ(0)=0, 0<ξ1<⋯<ξm−2<ρ(T). We obtain the existence of three positive solutions by using fixed-point theorem in cones. The conclusions in this paper essentially extend and improve the known results.
url http://dx.doi.org/10.1155/2009/123283
work_keys_str_mv AT jianliu triplepositivesolutionsforthirdordermpointboundaryvalueproblemsontimescales
AT fuyixu triplepositivesolutionsforthirdordermpointboundaryvalueproblemsontimescales
_version_ 1716758294768386048

Similar Items