Frontiers of Mathematics in China >

2023 , Vol. 18 >Issue 1: 63 - 74

DOI: https://doi.org/10.3868/S140-DDD-023-003-X

RESEARCH　ARTICLE

Dependence of eigenvalues of regular Sturm-Liouville operators on the boundary condition

  • Xinya YANG , 1,2
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  • 1. School of Mathematics and Statistics, Shaanxi Normal University, Xi’an 710119, China
  • 2. Shanxi Engineering Vocational College, Taiyuan 030009, China

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2023 Higher Education Press 2023
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Abstract

In this paper, we study the continuous dependence of eigenvalue of Sturm-Liouville differential operators on the boundary condition by using of implicit function theorem. The work not only provides a new and elementary proof of the above results, but also explicitly presents the expressions for derivatives of the n-th eigenvalue with respect to given parameters. Furthermore, we obtain the new results of the position and number of the generated double eigenvalues under the real coupled boundary condition.

Key words： Regular Sturm-Liouville operator; eigenvalue; implicit function theorem

Cite this article

Xinya YANG . Dependence of eigenvalues of regular Sturm-Liouville operators on the boundary condition[J]. Frontiers of Mathematics in China, 2023 , 18(1) : 63 -74 . DOI: 10.3868/S140-DDD-023-003-X

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (Grant No. 11571212). The author would like to thank Professor Guangsheng Wei for discussions and patient instructions to the paper.

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