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Spectral Properties of Discrete Sturm-Liouville Problems with two Squared Eigenparameter-Dependent Boundary Conditions

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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.

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Authors and Affiliations

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

    Chenghua Gao  (高承华), Yali Wang  (王雅丽) & Li Lv  (吕莉)

Authors
  1. Chenghua Gao  (高承华)
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  2. Yali Wang  (王雅丽)
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  3. Li Lv  (吕莉)
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Corresponding authors

Correspondence to Chenghua Gao  (高承华), Yali Wang  (王雅丽) or Li Lv  (吕莉).

Additional information

The authors are supported by National Natural Sciences Foundation of China (11961060, 11671322), and the Key Project of Natural Sciences Foundation of Gansu Province (18JR3RA084).

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Gao, C., Wang, Y. & Lv, L. Spectral Properties of Discrete Sturm-Liouville Problems with two Squared Eigenparameter-Dependent Boundary Conditions. Acta Math Sci 40, 755–781 (2020). https://doi.org/10.1007/s10473-020-0312-5

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  • DOI: https://doi.org/10.1007/s10473-020-0312-5

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