Existence of Positive Solutions of a Discrete Elastic Beam Equation
Let T be an integer with T≥5 and let T2={2,3,…,T}. We consider the existence of positive solutions of the nonlinear boundary value problems of fourth-order difference equations Δ4u(t−2)−ra(t)f(u(t))=0, t∈T2, u(1)=u(T+1)=Δ2u(0)=Δ2u(T)=0, where r is a constant, a:T2→(0,∞), and f:[0,∞)→[0,∞) is conti...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2010/582919 |
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| author | Ruyun Ma Jiemei Li Chenghua Gao |
| author_facet | Ruyun Ma Jiemei Li Chenghua Gao |
| author_sort | Ruyun Ma |
| collection | DOAJ |
| description | Let T be an integer with T≥5 and let T2={2,3,…,T}. We consider the existence of positive solutions of the nonlinear boundary value problems of fourth-order difference equations
Δ4u(t−2)−ra(t)f(u(t))=0, t∈T2,
u(1)=u(T+1)=Δ2u(0)=Δ2u(T)=0, where r is a constant, a:T2→(0,∞), and f:[0,∞)→[0,∞) is continuous. Our approaches are based on the Krein-Rutman theorem and the global bifurcation theorem. |
| format | Article |
| id | doaj-art-f2f2dc8155c04432a4076a7950181c77 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-f2f2dc8155c04432a4076a7950181c772025-02-03T01:01:40ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2010-01-01201010.1155/2010/582919582919Existence of Positive Solutions of a Discrete Elastic Beam EquationRuyun Ma0Jiemei Li1Chenghua Gao2Department of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaDepartment of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaDepartment of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaLet T be an integer with T≥5 and let T2={2,3,…,T}. We consider the existence of positive solutions of the nonlinear boundary value problems of fourth-order difference equations Δ4u(t−2)−ra(t)f(u(t))=0, t∈T2, u(1)=u(T+1)=Δ2u(0)=Δ2u(T)=0, where r is a constant, a:T2→(0,∞), and f:[0,∞)→[0,∞) is continuous. Our approaches are based on the Krein-Rutman theorem and the global bifurcation theorem.http://dx.doi.org/10.1155/2010/582919 |
| spellingShingle | Ruyun Ma Jiemei Li Chenghua Gao Existence of Positive Solutions of a Discrete Elastic Beam Equation Discrete Dynamics in Nature and Society |
| title | Existence of Positive Solutions of a Discrete Elastic Beam Equation |
| title_full | Existence of Positive Solutions of a Discrete Elastic Beam Equation |
| title_fullStr | Existence of Positive Solutions of a Discrete Elastic Beam Equation |
| title_full_unstemmed | Existence of Positive Solutions of a Discrete Elastic Beam Equation |
| title_short | Existence of Positive Solutions of a Discrete Elastic Beam Equation |
| title_sort | existence of positive solutions of a discrete elastic beam equation |
| url | http://dx.doi.org/10.1155/2010/582919 |
| work_keys_str_mv | AT ruyunma existenceofpositivesolutionsofadiscreteelasticbeamequation AT jiemeili existenceofpositivesolutionsofadiscreteelasticbeamequation AT chenghuagao existenceofpositivesolutionsofadiscreteelasticbeamequation |