FINITE SPECTRUM OF STURM-LIOUVILLE PROBLEMS WITH $ N $ TRANSMISSION CONDITIONS AND SPECTRAL PARAMETERS IN THE BOUNDARY CONDITIONS

Junwei Zhu; Lina Gu; Shengbiao Li

doi:10.11948/20240213

2025 Volume 15 Issue 1

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Article navigation > Journal of Applied Analysis & Computation > 2025 > 15(1): 605-623

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Junwei Zhu, Lina Gu, Shengbiao Li. FINITE SPECTRUM OF STURM-LIOUVILLE PROBLEMS WITH $ N $ TRANSMISSION CONDITIONS AND SPECTRAL PARAMETERS IN THE BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 605-623. doi: 10.11948/20240213

Citation:

Junwei Zhu, Lina Gu, Shengbiao Li. FINITE SPECTRUM OF STURM-LIOUVILLE PROBLEMS WITH $ N $ TRANSMISSION CONDITIONS AND SPECTRAL PARAMETERS IN THE BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 605-623. doi: 10.11948/20240213

FINITE SPECTRUM OF STURM-LIOUVILLE PROBLEMS WITH $ N $ TRANSMISSION CONDITIONS AND SPECTRAL PARAMETERS IN THE BOUNDARY CONDITIONS

1.
College of Arts and Sciences, YangLing Vocational & Technical College, 712100 Yangling, China
2.
College of Education, Lanzhou University of Arts and Sciences, 730030 Lanzhou, China

Author Bio: Email: 986273818@qq.com(L. Gu); Email: 76260338@qq.com(S. Li)
Corresponding author: Email: lutjwzhu@163.com(J. Zhu)
Fund Project: The authors were supported by National Natural Science Foundation of China (41772147), Education Technology Innovation Project of Gansu Province (2022A-174) and Yangling Vocational & Technical College scientific research fund project (ZK24-65, ZK23-49)

Abstract

Abstract

In this paper, we mainly study the finite spectrum of Sturm-Liouville problems with $ n $ transmission conditions and spectral parameters in the boundary conditions. For any positive integer $ n $ and a set of positive integers $ m_{i}, i=0, 1, \cdots, n $, it has at most $ m_{0}+m_{1}+\cdots+m_{n}+2n+1 $ eigenvalues. And further we show that these $ m_{0}+m_{1}+\cdots+m_{n}+2n+1 $ eigenvalues can be distributed arbitrarily throughout the complex plane in the non-self-adjoint case and anywhere along the real line in the self-adjoint case. The key to this analysis is an iterative construction of the characteristic function, the main tool used in this paper is Rouche's theorem and iterative construction of initial value.
- Transmission conditions /
- spectral parameters /
- Sturm-Liouville problems /
- characteristic function
MSC: 34B15

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References

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