{"title":"Finite Spectrum of Sturm–Liouville Problems with Transmission Conditions Dependent on the Spectral Parameter","authors":"Na Zhang, Ji-jun Ao","doi":"10.1080/01630563.2022.2150641","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, we mainly study the finite spectrum of Sturm–Liouville problems with transmission conditions dependent on the spectral parameter. By analyzing on the characteristic function, we prove that this kind of Sturm–Liouville problems consist of finite number of eigenvalue and these finite eigenvalues can be located anywhere in the complex plane. It is illustrated that the number of eigenvalues not only depends on the partition of the domain interval, but also depends on the transmission conditions dependent on the spectral parameter and the boundary conditions.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2022-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Numerical Functional Analysis and Optimization","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/01630563.2022.2150641","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 1
Abstract
Abstract In this paper, we mainly study the finite spectrum of Sturm–Liouville problems with transmission conditions dependent on the spectral parameter. By analyzing on the characteristic function, we prove that this kind of Sturm–Liouville problems consist of finite number of eigenvalue and these finite eigenvalues can be located anywhere in the complex plane. It is illustrated that the number of eigenvalues not only depends on the partition of the domain interval, but also depends on the transmission conditions dependent on the spectral parameter and the boundary conditions.
期刊介绍：
Numerical Functional Analysis and Optimization is a journal aimed at development and applications of functional analysis and operator-theoretic methods in numerical analysis, optimization and approximation theory, control theory, signal and image processing, inverse and ill-posed problems, applied and computational harmonic analysis, operator equations, and nonlinear functional analysis. Not all high-quality papers within the union of these fields are within the scope of NFAO. Generalizations and abstractions that significantly advance their fields and reinforce the concrete by providing new insight and important results for problems arising from applications are welcome. On the other hand, technical generalizations for their own sake with window dressing about applications, or variants of known results and algorithms, are not suitable for this journal.
Numerical Functional Analysis and Optimization publishes about 70 papers per year. It is our current policy to limit consideration to one submitted paper by any author/co-author per two consecutive years. Exception will be made for seminal papers.
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