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...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2009/123283 |
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| _version_ | 1832549483519410176 |
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| author | Jian Liu Fuyi Xu |
| author_facet | Jian Liu Fuyi Xu |
| author_sort | Jian Liu |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-f32b5f1ca7db41fea92f8ed3595485a5 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-f32b5f1ca7db41fea92f8ed3595485a52025-02-03T06:11:20ZengWileyDiscrete 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2009/123283 |
| work_keys_str_mv | AT jianliu triplepositivesolutionsforthirdordermpointboundaryvalueproblemsontimescales AT fuyixu triplepositivesolutionsforthirdordermpointboundaryvalueproblemsontimescales |