Existence of Positive Solutions of Lotka-Volterra Competition Model with Nonlinear Boundary Conditions
A Lotka-Volterra competition model with nonlinear boundary conditions is considered. First, by using upper and lower solutions method for nonlinear boundary problems, we investigate the existence of positive solutions in weak competition case. Next, we prove that -d1Δu=u(a1-b1u-c1v), x∈Ω; -d2Δv=v(a2...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/102180 |
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| _version_ | 1850173406925815808 |
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| author | Yang Zhang Mingxin Wang Yuwen Wang |
| author_facet | Yang Zhang Mingxin Wang Yuwen Wang |
| author_sort | Yang Zhang |
| collection | DOAJ |
| description | A Lotka-Volterra competition model with nonlinear boundary conditions is considered. First, by using upper and lower solutions method for nonlinear boundary problems, we investigate the existence of positive solutions in weak competition case. Next, we prove that -d1Δu=u(a1-b1u-c1v), x∈Ω; -d2Δv=v(a2-b2u-c2v), x∈Ω; ∂u/∂ν+f(u)=0, x∈∂Ω; ∂v/∂ν+g(v)=0, x∈∂Ω, has no positive solution when one of the diffusion coefficients is sufficiently large. |
| format | Article |
| id | doaj-art-cd6e69d441254b6ebb1137cc365c6ccf |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-cd6e69d441254b6ebb1137cc365c6ccf2025-08-20T02:19:51ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/102180102180Existence of Positive Solutions of Lotka-Volterra Competition Model with Nonlinear Boundary ConditionsYang Zhang0Mingxin Wang1Yuwen Wang2Natural Science Research Center, Harbin Institute of Technology, Harbin 150080, ChinaNatural Science Research Center, Harbin Institute of Technology, Harbin 150080, ChinaNatural Science Research Center, Harbin Institute of Technology, Harbin 150080, ChinaA Lotka-Volterra competition model with nonlinear boundary conditions is considered. First, by using upper and lower solutions method for nonlinear boundary problems, we investigate the existence of positive solutions in weak competition case. Next, we prove that -d1Δu=u(a1-b1u-c1v), x∈Ω; -d2Δv=v(a2-b2u-c2v), x∈Ω; ∂u/∂ν+f(u)=0, x∈∂Ω; ∂v/∂ν+g(v)=0, x∈∂Ω, has no positive solution when one of the diffusion coefficients is sufficiently large.http://dx.doi.org/10.1155/2014/102180 |
| spellingShingle | Yang Zhang Mingxin Wang Yuwen Wang Existence of Positive Solutions of Lotka-Volterra Competition Model with Nonlinear Boundary Conditions Abstract and Applied Analysis |
| title | Existence of Positive Solutions of Lotka-Volterra Competition Model with Nonlinear Boundary Conditions |
| title_full | Existence of Positive Solutions of Lotka-Volterra Competition Model with Nonlinear Boundary Conditions |
| title_fullStr | Existence of Positive Solutions of Lotka-Volterra Competition Model with Nonlinear Boundary Conditions |
| title_full_unstemmed | Existence of Positive Solutions of Lotka-Volterra Competition Model with Nonlinear Boundary Conditions |
| title_short | Existence of Positive Solutions of Lotka-Volterra Competition Model with Nonlinear Boundary Conditions |
| title_sort | existence of positive solutions of lotka volterra competition model with nonlinear boundary conditions |
| url | http://dx.doi.org/10.1155/2014/102180 |
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