INVERSE SPECTRAL PROBLEM FOR STURM-LIOUVILLE OPERATOR WITH BOTH JUMP CONDITIONS DEPENDENT ON THE SPECTRAL PARAMETER

Hui Zhao; Ji-Jun Ao

doi:10.11948/20240367

2025 Volume 15 Issue 4

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Hui Zhao, Ji-Jun Ao. INVERSE SPECTRAL PROBLEM FOR STURM-LIOUVILLE OPERATOR WITH BOTH JUMP CONDITIONS DEPENDENT ON THE SPECTRAL PARAMETER[J]. Journal of Applied Analysis & Computation, 2025, 15(4): 1961-1974. doi: 10.11948/20240367

Citation:

Hui Zhao, Ji-Jun Ao. INVERSE SPECTRAL PROBLEM FOR STURM-LIOUVILLE OPERATOR WITH BOTH JUMP CONDITIONS DEPENDENT ON THE SPECTRAL PARAMETER[J]. Journal of Applied Analysis & Computation, 2025, 15(4): 1961-1974. doi: 10.11948/20240367

INVERSE SPECTRAL PROBLEM FOR STURM-LIOUVILLE OPERATOR WITH BOTH JUMP CONDITIONS DEPENDENT ON THE SPECTRAL PARAMETER

Hui Zhao^1,,
Ji-Jun Ao^1, ,

1.
College of Sciences, Inner Mongolia University of Technology, Hohhot, Inner Mongolia 010051, China

Author Bio: Email: 15534445382@163.com(H. Zhao)
Corresponding author: Email: george_ao78@sohu.com(J.-J. Ao)
Fund Project: The authors were supported by National Natural Science Foundation of China (No. 12261066) and Natural Science Foundation of Inner Mongolia Autonomous Region (Nos. 2021MS01020, 2023LHMS01015)

Abstract

Abstract

The inverse spectral problem of Sturm-Liouville operator with both of the jump conditions dependent on the spectral parameter is investigated. Firstly, by theoretical operator formulation the self-adjointness of the problem is proven and then some of the eigenvalue properties, especially the asymptotic formulas of eigenvalues and eigenfunctions are given. Finally, the uniqueness theorems of the corresponding inverse problems are given by Weyl function theory and inverse spectral data approach.
- Inverse problem /
- Sturm-Liouville operator /
- Weyl function /
- eigenparameter-dependent jump conditions
MSC: 34A55, 34B24, 34L05, 47A45

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References

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