A. V. Arutyunov, Z. T. Zhukovskaya, S. E. Zhukovskiy
{"title":"On Nonlinear Boundary Value Problems for Differential Inclusions","authors":"A. V. Arutyunov, Z. T. Zhukovskaya, S. E. Zhukovskiy","doi":"10.1134/s00122661230110010","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider autonomous differential inclusions with nonlinear boundary conditions.\nSufficient conditions for the existence of solutions in the class of absolutely continuous functions\nare obtained for these inclusions. It is shown that the corresponding existence theorem applies to\nthe Cauchy problem and the antiperiodic boundary value problem. The result is used to derive a\nnew mean value inequality for continuously differentiable functions.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-29","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/s00122661230110010","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 autonomous differential inclusions with nonlinear boundary conditions.
Sufficient conditions for the existence of solutions in the class of absolutely continuous functions
are obtained for these inclusions. It is shown that the corresponding existence theorem applies to
the Cauchy problem and the antiperiodic boundary value problem. The result is used to derive a
new mean value inequality for continuously differentiable functions.
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