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<...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2010-01-01
|
| Series: | Advances in Difference Equations |
| Online Access: | http://dx.doi.org/10.1155/2010/381932 |
| Summary: | 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. |
|---|---|
| ISSN: | 1687-1839 1687-1847 |