{"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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-23","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/s0012266123090045","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","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.
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