传输条件依赖于谱参数的Sturm-Liouville问题的有限谱

IF 1.4 4区数学 Q2 MATHEMATICS, APPLIED

Numerical Functional Analysis and Optimization Pub Date : 2022-12-06 DOI:10.1080/01630563.2022.2150641

Na Zhang, Ji-jun Ao

{"title":"传输条件依赖于谱参数的Sturm-Liouville问题的有限谱","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":"44 1","pages":"21 - 35"},"PeriodicalIF":1.4000,"publicationDate":"2022-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"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\":\"44 1\",\"pages\":\"21 - 35\"},\"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}","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

摘要

摘要本文主要研究传输条件依赖于谱参数的Sturm–Liouville问题的有限谱。通过对特征函数的分析，我们证明了这类Sturm–Liouville问题由有限个特征值组成，并且这些有限的特征值可以位于复平面中的任何位置。结果表明，特征值的个数不仅取决于域区间的划分，还取决于依赖于谱参数和边界条件的传输条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Finite Spectrum of Sturm–Liouville Problems with Transmission Conditions Dependent on the Spectral Parameter

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Numerical Functional Analysis and Optimization 数学-应用数学

CiteScore

2.40

自引率

8.30%

发文量

审稿时长

6-12 weeks

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.