具有奇异势的 Sturm-Liouville 算子带参数问题解的渐近特性研究

Pub Date : 2024-07-08 DOI:10.1134/s0012266124030017

I. S. Lomov

{"title":"具有奇异势的 Sturm-Liouville 算子带参数问题解的渐近特性研究","authors":"I. S. Lomov","doi":"10.1134/s0012266124030017","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The Sturm–Liouville operator with a singular potential is defined on an interval of the real\nline. Transmission conditions are specified at an interior point of the interval. The operator\npotential may have a nonintegrable singularity. For the strong solution of the Cauchy problem for\nan equation with a parameter, asymptotic formulas and estimates are obtained on each of the\nsolution smoothness intervals.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Study of the Asymptotic Properties of the Solution to a Problem with a Parameter for the Sturm–Liouville Operator with a Singular Potential\",\"authors\":\"I. S. Lomov\",\"doi\":\"10.1134/s0012266124030017\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p> The Sturm–Liouville operator with a singular potential is defined on an interval of the real\\nline. Transmission conditions are specified at an interior point of the interval. The operator\\npotential may have a nonintegrable singularity. For the strong solution of the Cauchy problem for\\nan equation with a parameter, asymptotic formulas and estimates are obtained on each of the\\nsolution smoothness intervals.\\n</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-07-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s0012266124030017\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124030017","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

摘要带奇异势的 Sturm-Liouville 算子定义在一个重线段上。在区间的内点规定了传递条件。算子势可能具有不可解奇点。对于带参数方程的考希问题的强解，在每个解的平滑区间上都得到了渐近公式和估计值。

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

Study of the Asymptotic Properties of the Solution to a Problem with a Parameter for the Sturm–Liouville Operator with a Singular Potential

Abstract

The Sturm–Liouville operator with a singular potential is defined on an interval of the real line. Transmission conditions are specified at an interior point of the interval. The operator potential may have a nonintegrable singularity. For the strong solution of the Cauchy problem for an equation with a parameter, asymptotic formulas and estimates are obtained on each of the solution smoothness intervals.

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