Existence of Three Positive Solutions for m-Point Discrete Boundary Value Problems with p-Laplacian
We consider the multi-point discrete boundary value problem with one-dimensional p-Laplacian operator Δ(ϕp(Δu(t−1))+q(t)f(t,u(t),Δu(t))=0, t∈{1,…,n−1} subject to the boundary conditions: u(0)=0, u(n)=∑i=1m−2aiu(ξi), where ϕp(s)=|s|p−2s,p>1,ξi∈{2,…,n−2} with 1<ξ1<⋯<ξm−2<n−1 and ai∈(0,1...
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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/10.1155/2009/538431 |
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| author | Yanping Guo Wenying Wei Yuerong Chen |
| author_facet | Yanping Guo Wenying Wei Yuerong Chen |
| author_sort | Yanping Guo |
| collection | DOAJ |
| description | We consider the multi-point discrete boundary value problem with one-dimensional p-Laplacian operator
Δ(ϕp(Δu(t−1))+q(t)f(t,u(t),Δu(t))=0, t∈{1,…,n−1} subject to the boundary conditions: u(0)=0, u(n)=∑i=1m−2aiu(ξi), where ϕp(s)=|s|p−2s,p>1,ξi∈{2,…,n−2} with 1<ξ1<⋯<ξm−2<n−1 and ai∈(0,1),0<∑i=1m−2ai<1. Using a new fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions to the above boundary value problem. |
| format | Article |
| id | doaj-art-53ffec62c50f46f5a3f5e98342a0fc18 |
| 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-53ffec62c50f46f5a3f5e98342a0fc182025-02-03T01:10:44ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2009-01-01200910.1155/2009/538431538431Existence of Three Positive Solutions for m-Point Discrete Boundary Value Problems with p-LaplacianYanping Guo0Wenying Wei1Yuerong Chen2College of Sciences, Hebei University of Science and Technology, Shijiazhuang, Hebei 050018, ChinaCollege of Sciences, Hebei University of Science and Technology, Shijiazhuang, Hebei 050018, ChinaCollege of Sciences, Hebei University of Science and Technology, Shijiazhuang, Hebei 050018, ChinaWe consider the multi-point discrete boundary value problem with one-dimensional p-Laplacian operator Δ(ϕp(Δu(t−1))+q(t)f(t,u(t),Δu(t))=0, t∈{1,…,n−1} subject to the boundary conditions: u(0)=0, u(n)=∑i=1m−2aiu(ξi), where ϕp(s)=|s|p−2s,p>1,ξi∈{2,…,n−2} with 1<ξ1<⋯<ξm−2<n−1 and ai∈(0,1),0<∑i=1m−2ai<1. Using a new fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions to the above boundary value problem.http://dx.doi.org/10.1155/2009/538431 |
| spellingShingle | Yanping Guo Wenying Wei Yuerong Chen Existence of Three Positive Solutions for m-Point Discrete Boundary Value Problems with p-Laplacian Discrete Dynamics in Nature and Society |
| title | Existence of Three Positive Solutions for m-Point Discrete Boundary Value Problems with p-Laplacian |
| title_full | Existence of Three Positive Solutions for m-Point Discrete Boundary Value Problems with p-Laplacian |
| title_fullStr | Existence of Three Positive Solutions for m-Point Discrete Boundary Value Problems with p-Laplacian |
| title_full_unstemmed | Existence of Three Positive Solutions for m-Point Discrete Boundary Value Problems with p-Laplacian |
| title_short | Existence of Three Positive Solutions for m-Point Discrete Boundary Value Problems with p-Laplacian |
| title_sort | existence of three positive solutions for m point discrete boundary value problems with p laplacian |
| url | http://dx.doi.org/10.1155/2009/538431 |
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