{"title":"CONTINUOUS BRANCHES OF MULTIVALUED MAPPINGS AND FUNCTIONAL-DIFFERENTIAL INCLUSIONS WITH NONCONVEX RIGHT-HAND SIDE","authors":"A. Bulgakov","doi":"10.1070/SM1992V071N02ABEH001398","DOIUrl":null,"url":null,"abstract":"It is proved that in the space of Bochner-integrable mappings a multivalued mapping with nonconvex images has a continuous branch that, for a given single-valued mapping and for a previously specified accuracy, realizes the distance between the images of the single-valued mapping and the multivalued mapping. This result is applied to the investigation of properties of solutions of functional-differential inclusions with nonconvex right-hand side.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"32 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1992-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-sbornik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/SM1992V071N02ABEH001398","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 5
Abstract
It is proved that in the space of Bochner-integrable mappings a multivalued mapping with nonconvex images has a continuous branch that, for a given single-valued mapping and for a previously specified accuracy, realizes the distance between the images of the single-valued mapping and the multivalued mapping. This result is applied to the investigation of properties of solutions of functional-differential inclusions with nonconvex right-hand side.
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