{"title":"YERS–ULAM–RASSIAS STABILITY OF NONLINEAR DIFFERENTIAL EQUATIONS WITH A GENERALIZED ACTIONS ON THE RIGHT-HAND SIDE","authors":"A. Sesekin, Anna D. Kandrina","doi":"10.15826/umj.2023.1.013","DOIUrl":null,"url":null,"abstract":"The paper considers the Hyers–Ulam–Rassias stability for systems of nonlinear differential equations with a generalized action on the right-hand side, for example, containing impulses — delta functions. The fact that the derivatives in the equation are considered distributions required a correction of the well known Hyers–Ulam–Rassias definition of stability for such equations. Sufficient conditions are obtained that ensure the property under study.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ural Mathematical Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15826/umj.2023.1.013","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
The paper considers the Hyers–Ulam–Rassias stability for systems of nonlinear differential equations with a generalized action on the right-hand side, for example, containing impulses — delta functions. The fact that the derivatives in the equation are considered distributions required a correction of the well known Hyers–Ulam–Rassias definition of stability for such equations. Sufficient conditions are obtained that ensure the property under study.
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