Eigenvalues of Sturm-Liouville problems with eigenparameter dependent boundary and interface conditions

In this paper, a regular discontinuous Sturm-Liouville problem which contains eigenparameter in both boundary and interface conditions is investigated. Firstly, a new operator associated with the problem is constructed, and the self-adjointness of the operator in an appropriate Hilbert space is prov...

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Published inMathematical modelling and analysis Vol. 28; no. 3; pp. 374 - 392
Main Authors Zheng, Jiajia, Li, Kun, Zheng, Zhaowen
Format Journal Article
LanguageEnglish
Published Vilnius Vilnius Gediminas Technical University 04.09.2023
Subjects
Analysis
Boundary conditions
Boundary value problems
continuity
differential expression
Eigenvalues
Eigenvectors
Hilbert space
interface conditions
Operators (mathematics)
Parameter estimation
Sturm-Liouville problems
China
continuity
differential expression
interface conditions
Sturm-Liouville problems
Online AccessGet full text
ISSN1392-6292
1648-3510
DOI10.3846/mma.2023.17094

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Abstract In this paper, a regular discontinuous Sturm-Liouville problem which contains eigenparameter in both boundary and interface conditions is investigated. Firstly, a new operator associated with the problem is constructed, and the self-adjointness of the operator in an appropriate Hilbert space is proved. Some properties of eigenvalues are discussed. Finally, the continuity of eigenvalues and eigenfunctions is investigated, and the differential expressions in the sense of ordinary or Fréchet of the eigenvalues concerning the data are given.
AbstractList In this paper, a regular discontinuous Sturm-Liouville problem which contains eigenparameter in both boundary and interface conditions is investigated. Firstly, a new operator associated with the problem is constructed, and the self-adjointness of the operator in an appropriate Hilbert space is proved. Some properties of eigenvalues are discussed. Finally, the continuity of eigenvalues and eigenfunctions is investigated, and the differential expressions in the sense of ordinary or Fréchet of the eigenvalues concerning the data are given.
In this paper, a regular discontinuous Sturm-Liouville problem which contains eigenparameter in both boundary and interface conditions is investigated. Firstly, a new operator associated with the problem is constructed, and the self-adjointness of the operator in an appropriate Hilbert space is proved. Some properties of eigenvalues are discussed. Finally, the continuity of eigenvalues and eigenfunctions is investigated, and the differential expressions in the sense of ordinary or Frechet of the eigenvalues concerning the data are given. Keywords: Sturm-Liouville problems, interface conditions, continuity, differential expression. AMS Subject Classification: 34L05; 34L10; 34L15.
Audience Academic
Author Zheng, Jiajia
Li, Kun
Zheng, Zhaowen
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  fullname: Zheng, Zhaowen
  organization: College of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou, China
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SubjectTerms Analysis
Boundary conditions
Boundary value problems
continuity
differential expression
Eigenvalues
Eigenvectors
Hilbert space
interface conditions
Operators (mathematics)
Parameter estimation
Sturm-Liouville problems
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