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| Eigenvalues of Second-Order Left-Definite Linear Difference Operatorwith Spectral Parameters in Boundary Conditions |
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Citation： |
Chenghua GAO,Jingjing WANG,Xiaobin YAO,Xueqin CAO.Eigenvalues of Second-Order Left-Definite Linear Difference Operatorwith Spectral Parameters in Boundary Conditions[J].Chinese Annals of Mathematics B,2024,45(6):905~926 |
| Page view： 811
Net amount： 265 |
Authors： |
Chenghua GAO; Jingjing WANG;Xiaobin YAO;Xueqin CAO |
Foundation： |
the National Natural Science Foundation of China (Nos. 12461039,
12161071), the Doctoral Research Fund Project of Lanzhou City University (No. LZCU-BS2023-24),
the Youth Fund Project of Lanzhou City University (No. LZCU-QN2023-09), Gansu Youth Science and
Technology Fund Project (No. 24JRRA536) and the Discipline Construction Project of Lanzhou City
University |
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| Abstract： |
In this paper, the authors consider the spectra of second-order left-definite difference operator with linear spectral parameters in two boundary conditions. First, they
obtain the exact number of this kind of eigenvalue problem, and prove these eigenvalues
are all real and simple. In details, they get that the number of the positive (negative)
eigenvalues is related to not only the number of positive (negative) elements in the weight
function, but also the parameters in the boundary conditions. Second, they obtain the
interlacing properties of these eigenvalues and the sign-changing properties of the corresponding eigenfunctions according to the relations of the parameters in the boundary
conditions. |
Keywords： |
Left-definite difference operator, Boundary conditions with spectral parameters, Interlacing properties, Oscillation properties |
Classification： |
39A06, 39A12, 39A21, 39A70 |
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