数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (3): 755-781.doi: 10.1007/s10473-020-0312-5

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

高承华, 王雅丽, 吕莉   

  1. Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
  • 收稿日期:2018-12-27 修回日期:2019-07-13 出版日期:2020-06-25 发布日期:2020-07-17
  • 通讯作者: Chenghua GAO E-mail:gaokuguo@163.com
  • 作者简介:Yali WANG,E-mail:18209319069@163.com;Li LV,E-mail:15101211660@163.com
  • 基金资助:
    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).

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

Chenghua GAO, Yali WANG, Li LV   

  1. Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
  • Received:2018-12-27 Revised:2019-07-13 Online:2020-06-25 Published:2020-07-17
  • Contact: Chenghua GAO E-mail:gaokuguo@163.com
  • Supported by:
    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).

摘要: 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.

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

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

中图分类号: 

  • 39A10