Structure of Eigenvalues of Multi-Point Boundary Value Problems
The structure of eigenvalues of −y″+q(x)y=λy, y(0)=0, and y(1)=∑k=1mαky(ηk), will be studied, where q∈L1([0,1],ℝ), α=(αk)∈ℝm, and 0<η1<...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2010-01-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://dx.doi.org/10.1155/2010/381932 |
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doaj-eeb6e8711e2545a19d3306f8bbad04592020-11-24T21:53:01ZengSpringerOpenAdvances in Difference Equations1687-18391687-18472010-01-01201010.1155/2010/381932Structure of Eigenvalues of Multi-Point Boundary Value ProblemsMeirong ZhangDongmei SunJie GaoThe structure of eigenvalues of −y″+q(x)y=λy, y(0)=0, and y(1)=∑k=1mαky(ηk), will be studied, where q∈L1([0,1],ℝ), α=(αk)∈ℝm, and 0<η1<⋯<ηm<1. Due to the nonsymmetry of the problem, this equation may admit complex eigenvalues. In this paper, a complete structure of all complex eigenvalues of this equation will be obtained. In particular, it is proved that this equation has always a sequence of real eigenvalues tending to +∞. Moreover, there exists some constant Aq>0 depending on q, such that when α satisfies ‖α‖≤Aq, all eigenvalues of this equation are necessarily real. http://dx.doi.org/10.1155/2010/381932 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Meirong Zhang Dongmei Sun Jie Gao |
| spellingShingle |
Meirong Zhang Dongmei Sun Jie Gao Structure of Eigenvalues of Multi-Point Boundary Value Problems Advances in Difference Equations |
| author_facet |
Meirong Zhang Dongmei Sun Jie Gao |
| author_sort |
Meirong Zhang |
| title |
Structure of Eigenvalues of Multi-Point Boundary Value Problems |
| title_short |
Structure of Eigenvalues of Multi-Point Boundary Value Problems |
| title_full |
Structure of Eigenvalues of Multi-Point Boundary Value Problems |
| title_fullStr |
Structure of Eigenvalues of Multi-Point Boundary Value Problems |
| title_full_unstemmed |
Structure of Eigenvalues of Multi-Point Boundary Value Problems |
| title_sort |
structure of eigenvalues of multi-point boundary value problems |
| publisher |
SpringerOpen |
| series |
Advances in Difference Equations |
| issn |
1687-1839 1687-1847 |
| publishDate |
2010-01-01 |
| description |
The structure of eigenvalues of −y″+q(x)y=λy, y(0)=0, and y(1)=∑k=1mαky(ηk), will be studied, where q∈L1([0,1],ℝ), α=(αk)∈ℝm, and 0<η1<⋯<ηm<1. Due to the nonsymmetry of the problem, this equation may admit complex eigenvalues. In this paper, a complete structure of all complex eigenvalues of this equation will be obtained. In particular, it is proved that this equation has always a sequence of real eigenvalues tending to +∞. Moreover, there exists some constant Aq>0 depending on q, such that when α satisfies ‖α‖≤Aq, all eigenvalues of this equation are necessarily real. |
| url |
http://dx.doi.org/10.1155/2010/381932 |
| work_keys_str_mv |
AT meirongzhang structureofeigenvaluesofmultipointboundaryvalueproblems AT dongmeisun structureofeigenvaluesofmultipointboundaryvalueproblems AT jiegao structureofeigenvaluesofmultipointboundaryvalueproblems |
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1725873341739302912 |