具有两个内点不连续性的Sturm-Liouville问题

Q4 Mathematics

Journal of the Indian Mathematical Society Pub Date : 2018-01-04 DOI:10.18311/JIMS/2018/14940

Hongmei Han

{"title":"具有两个内点不连续性的Sturm-Liouville问题","authors":"Hongmei Han","doi":"10.18311/JIMS/2018/14940","DOIUrl":null,"url":null,"abstract":"In this paper, we study the Sturm-Liouville operator with eigenparameter-dependent boundary conditions and transmission conditions at two interior points. We establish a new operator A associated with the problem, prove the operator A is self-adjoint in an appropriate space H , construct the basic solutions and investigate some properties of the eigenvalues and corresponding eigenfunctions, then obtain asymptotic formulas for the eigenvalues and eigenfunctions, its Green function and the resolvent operator are also involved.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2018-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Sturm-Liouville Problems with Discontinuities at Two Interior Points\",\"authors\":\"Hongmei Han\",\"doi\":\"10.18311/JIMS/2018/14940\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we study the Sturm-Liouville operator with eigenparameter-dependent boundary conditions and transmission conditions at two interior points. We establish a new operator A associated with the problem, prove the operator A is self-adjoint in an appropriate space H , construct the basic solutions and investigate some properties of the eigenvalues and corresponding eigenfunctions, then obtain asymptotic formulas for the eigenvalues and eigenfunctions, its Green function and the resolvent operator are also involved.\",\"PeriodicalId\":38246,\"journal\":{\"name\":\"Journal of the Indian Mathematical Society\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-01-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Indian Mathematical Society\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.18311/JIMS/2018/14940\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Indian Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.18311/JIMS/2018/14940","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 0

摘要

本文研究了具有本征参数相关边界条件和两个内点传输条件的Sturm-Liouville算子。我们建立了一个与该问题相关的新算子a，证明了算子a在适当的空间H中是自伴的，构造了基本解，研究了特征值和相应特征函数的一些性质，得到了特征值与特征函数的渐近公式，它的格林函数和预解算子也涉及其中。

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

Sturm-Liouville Problems with Discontinuities at Two Interior Points

In this paper, we study the Sturm-Liouville operator with eigenparameter-dependent boundary conditions and transmission conditions at two interior points. We establish a new operator A associated with the problem, prove the operator A is self-adjoint in an appropriate space H , construct the basic solutions and investigate some properties of the eigenvalues and corresponding eigenfunctions, then obtain asymptotic formulas for the eigenvalues and eigenfunctions, its Green function and the resolvent operator are also involved.

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

Journal of the Indian Mathematical Society Mathematics-Mathematics (all)

CiteScore

0.50

自引率

0.00%

发文量

期刊介绍： The Society began publishing Progress Reports right from 1907 and then the Journal from 1908 (The 1908 and 1909 issues of the Journal are entitled "The Journal of the Indian Mathematical Club"). From 1910 onwards,it is published as its current title ''the Journal of Indian Mathematical Society. The four issues of the Journal constitute a single volume and it is published in two parts: issues 1 and 2 (January to June) as one part and issues 3 and 4 (July to December) as the second part. The four issues of the Mathematics Student (another periodical of the Society) are published as a single yearly volume. Only the original research papers of high quality are published in the Journal of Indian Mathematical Society.