Positive Solutions for Third-Order Nonlinear p-Laplacian m-Point Boundary Value Problems on Time Scales
We study the following third-order p-Laplacian m-point boundary value problems on time scales: (ϕp(uΔ∇))∇+a(t)f(t,u(t))=0, t∈[0,T]T, βu(0)−γuΔ(0)=0, u(T)=∑i=1m−2aiu(ξi), ϕp(uΔ∇(0))=∑i=1m−2biϕp(uΔ∇(ξi)), where ϕp(s) is p-Laplacian operator, that is, ϕp(s)=|s|p−2s, p>1, ϕp−1=ϕq, 1/p+1/q=1, 0<ξ...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2008/143040 |
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| author | Fuyi Xu |
| author_facet | Fuyi Xu |
| author_sort | Fuyi Xu |
| collection | DOAJ |
| description | We study the following third-order p-Laplacian m-point boundary value problems on time scales: (ϕp(uΔ∇))∇+a(t)f(t,u(t))=0, t∈[0,T]T, βu(0)−γuΔ(0)=0, u(T)=∑i=1m−2aiu(ξi), ϕp(uΔ∇(0))=∑i=1m−2biϕp(uΔ∇(ξi)), where ϕp(s) is p-Laplacian operator, that is, ϕp(s)=|s|p−2s, p>1, ϕp−1=ϕq, 1/p+1/q=1, 0<ξ1<⋯<ξm−2<ρ(T). We obtain the existence of 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-a2cecde8faf34576a64e8e5480adac9e |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-a2cecde8faf34576a64e8e5480adac9e2025-02-03T07:25:14ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2008-01-01200810.1155/2008/143040143040Positive Solutions for Third-Order Nonlinear p-Laplacian m-Point Boundary Value Problems on Time ScalesFuyi Xu0School of Mathematics and Information Science, Shandong University of Technology, Zibo, Shandong 255049, ChinaWe study the following third-order p-Laplacian m-point boundary value problems on time scales: (ϕp(uΔ∇))∇+a(t)f(t,u(t))=0, t∈[0,T]T, βu(0)−γuΔ(0)=0, u(T)=∑i=1m−2aiu(ξi), ϕp(uΔ∇(0))=∑i=1m−2biϕp(uΔ∇(ξi)), where ϕp(s) is p-Laplacian operator, that is, ϕp(s)=|s|p−2s, p>1, ϕp−1=ϕq, 1/p+1/q=1, 0<ξ1<⋯<ξm−2<ρ(T). We obtain the existence of 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/10.1155/2008/143040 |
| spellingShingle | Fuyi Xu Positive Solutions for Third-Order Nonlinear p-Laplacian m-Point Boundary Value Problems on Time Scales Discrete Dynamics in Nature and Society |
| title | Positive Solutions for Third-Order Nonlinear p-Laplacian m-Point Boundary Value Problems on Time Scales |
| title_full | Positive Solutions for Third-Order Nonlinear p-Laplacian m-Point Boundary Value Problems on Time Scales |
| title_fullStr | Positive Solutions for Third-Order Nonlinear p-Laplacian m-Point Boundary Value Problems on Time Scales |
| title_full_unstemmed | Positive Solutions for Third-Order Nonlinear p-Laplacian m-Point Boundary Value Problems on Time Scales |
| title_short | Positive Solutions for Third-Order Nonlinear p-Laplacian m-Point Boundary Value Problems on Time Scales |
| title_sort | positive solutions for third order nonlinear p laplacian m point boundary value problems on time scales |
| url | http://dx.doi.org/10.1155/2008/143040 |
| work_keys_str_mv | AT fuyixu positivesolutionsforthirdordernonlinearplaplacianmpointboundaryvalueproblemsontimescales |