SPECTRAL PROPERTIES OF DISCRETE STURM-LIOUVILLE PROBLEMS WITH TWO SQUARED EIGENPARAMETER-DEPENDENT BOUNDARY CONDITIONS

doi:10.1007/s10473-020-0312-5

Abstract

Abstract: In this article, we consider a discrete right-definite Sturm-Liouville problems with two squared eigenparameter-dependent boundary conditions. By constructing some new Lagrange-type identities and two fundamental functions, we obtain not only the existence, the simplicity, and the interlacing properties of the real eigenvalues, but also the oscillation properties, orthogonality of the eigenfunctions, and the expansion theorem. Finally, we also give a computation scheme for computing eigenvalues and eigenfunctions of specific eigenvalue problems.

Key words: Discrete Sturm-Liouville problems, squared eigenparameter-dependent boundary conditions, interlacing, oscillation properties, orthogonality

CLC Number:

39A10

Chenghua GAO, Yali WANG, Li LV. SPECTRAL PROPERTIES OF DISCRETE STURM-LIOUVILLE PROBLEMS WITH TWO SQUARED EIGENPARAMETER-DEPENDENT BOUNDARY CONDITIONS[J].Acta mathematica scientia,Series B, 2020, 40(3): 755-781.

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