Spectral analysis of discontinuous Sturm-Liouville operators with Herglotzs transmission

Gaofeng Du; Chenghua Gao; Jingjing Wang; Gaofeng Du; Chenghua Gao; Jingjing Wang

doi:10.3934/era.2023108

Electronic Research Archive

2023, Volume 31, Issue 4: 2108-2119. doi: 10.3934/era.2023108

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Spectral analysis of discontinuous Sturm-Liouville operators with Herglotzs transmission

Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Received: 18 November 2022 Revised: 06 February 2023 Accepted: 08 February 2023 Published: 17 February 2023

In this paper, we study the spectral properties of the Sturm-Liouville operator with eigenparameter-dependent boundary conditions and transmission conditions. In details, we introduce a Hilbert space formula, so that the problem we consider can be interpreted as an eigenvalue problem of an self-adjoint operator. Moreover, the Green's function and the resolvent of the related linear operator are obtained.
- spectral analysis,
- Sturm-Liouville operator,
- transmission conditions,
- eigenparameter dependent boundary condition,
- eigenvalue problem
Citation: Gaofeng Du, Chenghua Gao, Jingjing Wang. Spectral analysis of discontinuous Sturm-Liouville operators with Herglotzs transmission[J]. Electronic Research Archive, 2023, 31(4): 2108-2119. doi: 10.3934/era.2023108

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Abstract

In this paper, we study the spectral properties of the Sturm-Liouville operator with eigenparameter-dependent boundary conditions and transmission conditions. In details, we introduce a Hilbert space formula, so that the problem we consider can be interpreted as an eigenvalue problem of an self-adjoint operator. Moreover, the Green's function and the resolvent of the related linear operator are obtained.

References

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