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

doi:10.3868/S140-DDD-023-003-X

Front. Math. China

2023, Vol. 18

Issue (1) : 63-74 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(

)

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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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.

Keywords Regular Sturm-Liouville operator eigenvalue implicit function theorem

Online First Date: 22 May 2023 Issue Date: 31 May 2023

Cite this article:

Xinya YANG. Dependence of eigenvalues of regular Sturm-Liouville operators on the boundary condition[J]. Front. Math. China, 2023, 18(1): 63-74.

URL:

https://academic.hep.com.cn/fmc/EN/10.3868/S140-DDD-023-003-X
https://academic.hep.com.cn/fmc/EN/Y2023/V18/I1/63

Fig.1 The relation of eigenvalues

λ n = λ n (k)

and

λ n + 1 = λ n + 1 (k)

μ n = ν n + 1

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