{"title":"Averaging of a Normal System of Ordinary Differential Equations of High Frequency with a Multipoint Boundary Value Problem on a Semiaxis","authors":"V. B. Levenshtam","doi":"10.3103/s1066369x2470018x","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A multipoint boundary value problem for a nonlinear normal system of ordinary differential equations with a rapidly time-oscillating right-hand side is considered on a positive time semiaxis. For this problem, which depends on a large parameter (high oscillation frequency), a limiting (averaged) multipoint boundary value problem is constructed and a limiting transition in the Hölder space of bounded vector functions defined on the considered semiaxis is justified. Thus, for normal systems of differential equations in the case of a multipoint boundary value problem, the Krylov–Bogolyubov averaging method on the semiaxis is justified.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":"12 7 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s1066369x2470018x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
A multipoint boundary value problem for a nonlinear normal system of ordinary differential equations with a rapidly time-oscillating right-hand side is considered on a positive time semiaxis. For this problem, which depends on a large parameter (high oscillation frequency), a limiting (averaged) multipoint boundary value problem is constructed and a limiting transition in the Hölder space of bounded vector functions defined on the considered semiaxis is justified. Thus, for normal systems of differential equations in the case of a multipoint boundary value problem, the Krylov–Bogolyubov averaging method on the semiaxis is justified.
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