{"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":50580,"journal":{"name":"Differential Equations","volume":"30 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124030017","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍：
Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.
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