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Eigenvalues of Second-Order Left-Definite Linear Difference Operator with Spectral Parameters in Boundary Conditions

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Eigenvalues of Second-Order Left-Definite Linear Difference Operator with Spectral Parameters in Boundary Conditions
In this paper,the authors consider the spectra of second-order left-definite d-ifference 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 cor-responding eigenfunctions according to the relations of the parameters in the boundary conditions.

Left-definite difference operatorBoundary conditions with spectral pa-rametersInterlacing propertiesOscillation properties

Chenghua GAO、Jingjing WANG、Xiaobin YAO、Xueqin CAO

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Department of Mathematics,Northwest Normal University,Lanzhou 730070,China

School of Information Engineering,Lanzhou City University,Lanzhou 730070,China

Department of Mathematics,Qinghai Minzu University,Xining 810007,China

Left-definite difference operator Boundary conditions with spectral pa-rameters Interlacing properties Oscillation properties

2024

10.1007/s11401-024-0044-2

数学年刊B辑(英文版)
国家教育部委托复旦大学主办

数学年刊B辑(英文版)

CSTPCD
影响因子：0.129
ISSN：0252-9599
年,卷(期)：2024.45(6)