{"title":"广义作用在右手边的非线性微分方程的YERS–ULAM–RASSIAS稳定性","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":"{\"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}","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}
YERS–ULAM–RASSIAS STABILITY OF NONLINEAR DIFFERENTIAL EQUATIONS WITH A GENERALIZED ACTIONS ON THE RIGHT-HAND SIDE
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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