{"title":"Approximation to the Sturm–Liouville Problem with a Discontinuous Nonlinearity","authors":"D. K. Potapov","doi":"10.1134/s0012266123090045","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider a continuous approximation to the Sturm–Liouville problem with\na nonlinearity discontinuous in the phase variable. The approximating problem is obtained from\nthe original one by small perturbations of the spectral parameter and by approximating the\nnonlinearity by Carathéodory functions. The variational method is used to prove the\ntheorem on the proximity of solutions of the approximating and original problems. The resulting\ntheorem is applied to the one-dimensional Gol’dshtik and Lavrent’ev models of separated flows.\n</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":"104 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2023-11-23","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/s0012266123090045","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
We consider a continuous approximation to the Sturm–Liouville problem with
a nonlinearity discontinuous in the phase variable. The approximating problem is obtained from
the original one by small perturbations of the spectral parameter and by approximating the
nonlinearity by Carathéodory functions. The variational method is used to prove the
theorem on the proximity of solutions of the approximating and original problems. The resulting
theorem is applied to the one-dimensional Gol’dshtik and Lavrent’ev models of separated flows.
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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