Global Bifurcation in 2m-Order Generic Systems of Nonlinear Boundary Value Problems
We consider the systems of (-1)mu(2m)=λu+λv+uf(t,u,v), t∈(0,1), u(2i)(0)=u(2i)(1)=0, and 0≤i≤m-1, (-1)mv(2m)=μu+μv+vg(t, u,v), t∈(0,1), v(2i)(0)=v(2i)(1)=0, 0≤i≤m-1, where λ,μ∈R are real parameters. f,g:[0,1]×R2→R are Ck,k≥3 functions and f(t,0,0)=g(t,0,0)=0,t∈[0,1]. It will be shown that if t...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/804619 |
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| author | Xiaoling Han Jia Xu Guowei Dai |
| author_facet | Xiaoling Han Jia Xu Guowei Dai |
| author_sort | Xiaoling Han |
| collection | DOAJ |
| description | We consider the systems of (-1)mu(2m)=λu+λv+uf(t,u,v), t∈(0,1), u(2i)(0)=u(2i)(1)=0, and 0≤i≤m-1, (-1)mv(2m)=μu+μv+vg(t, u,v), t∈(0,1), v(2i)(0)=v(2i)(1)=0, 0≤i≤m-1, where λ,μ∈R are real parameters. f,g:[0,1]×R2→R are Ck,k≥3 functions and f(t,0,0)=g(t,0,0)=0,t∈[0,1]. It will be shown that if the functions, f and g are “generic” then the solution set of the systems consists of a countable collection of 2-dimensional, Ck manifolds. |
| format | Article |
| id | doaj-art-32ba318fd2054d718cfb9c3de9f49434 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-32ba318fd2054d718cfb9c3de9f494342025-02-03T01:29:13ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/804619804619Global Bifurcation in 2m-Order Generic Systems of Nonlinear Boundary Value ProblemsXiaoling Han0Jia Xu1Guowei Dai2College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, ChinaCollege of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, ChinaCollege of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, ChinaWe consider the systems of (-1)mu(2m)=λu+λv+uf(t,u,v), t∈(0,1), u(2i)(0)=u(2i)(1)=0, and 0≤i≤m-1, (-1)mv(2m)=μu+μv+vg(t, u,v), t∈(0,1), v(2i)(0)=v(2i)(1)=0, 0≤i≤m-1, where λ,μ∈R are real parameters. f,g:[0,1]×R2→R are Ck,k≥3 functions and f(t,0,0)=g(t,0,0)=0,t∈[0,1]. It will be shown that if the functions, f and g are “generic” then the solution set of the systems consists of a countable collection of 2-dimensional, Ck manifolds.http://dx.doi.org/10.1155/2012/804619 |
| spellingShingle | Xiaoling Han Jia Xu Guowei Dai Global Bifurcation in 2m-Order Generic Systems of Nonlinear Boundary Value Problems Abstract and Applied Analysis |
| title | Global Bifurcation in 2m-Order Generic Systems of Nonlinear Boundary Value Problems |
| title_full | Global Bifurcation in 2m-Order Generic Systems of Nonlinear Boundary Value Problems |
| title_fullStr | Global Bifurcation in 2m-Order Generic Systems of Nonlinear Boundary Value Problems |
| title_full_unstemmed | Global Bifurcation in 2m-Order Generic Systems of Nonlinear Boundary Value Problems |
| title_short | Global Bifurcation in 2m-Order Generic Systems of Nonlinear Boundary Value Problems |
| title_sort | global bifurcation in 2m order generic systems of nonlinear boundary value problems |
| url | http://dx.doi.org/10.1155/2012/804619 |
| work_keys_str_mv | AT xiaolinghan globalbifurcationin2mordergenericsystemsofnonlinearboundaryvalueproblems AT jiaxu globalbifurcationin2mordergenericsystemsofnonlinearboundaryvalueproblems AT guoweidai globalbifurcationin2mordergenericsystemsofnonlinearboundaryvalueproblems |