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Research Article | Open Access

Spectral analysis of discontinuous Sturm-Liouville operators with Herglotzs transmission

Gaofeng Du, Chenghua Gao( ), Jingjing Wang
Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
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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.

Keywords

spectral analysisSturm-Liouville operatortransmission conditionseigenparameter dependent boundary conditioneigenvalue problem

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Electronic Research Archive
Volume 31 Issue 4,
April 2023
Pages 2108-2119
DOI: 10.3934/era.2023108

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Cite this article:
Du G, Gao C, Wang J. Spectral analysis of discontinuous Sturm-Liouville operators with Herglotzs transmission. Electronic Research Archive, 2023, 31(4): 2108-2119. https://doi.org/10.3934/era.2023108

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Received: 18 November 2022
Revised: 06 February 2023
Accepted: 08 February 2023
Published: 15 April 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)