Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2019, Volume 165, Pages 21–33
DOI: https://doi.org/10.36535/0233-6723-2019-165-21-33 (Mi into464) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Applications of covering mappings in the theory of implicit differential equations

E. O. Burlakova, T. V. Zhukovskayab, E. S. Zhukovskiyc, N. P. Puchkovb

a Tyumen State University
b Tambov State Technical University
c Tambov State University named after G.R. Derzhavin
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DOI: https://doi.org/10.36535/0233-6723-2019-165-21-33
Abstract: This paper is a brief review of results in the theory of covering mappings of metric spaces and vector metric spaces and its applications to implicit differential equations. For the Cauchy problem and boundary-value problems, we obtain existence conditions, estimates of solutions, and conditions of the continuous dependence of solutions on the parameters of the equation and initial and boundary conditions.
Keywords: covering mapping, map coincidence point, metric space, partially ordered space, implicit differential equation, Cauchy problem, boundary-value problem.
Funding agency Grant number
Russian Foundation for Basic Research 18-31-00227_мол_а
17-01-00553_а
17-41-680975_р_а
17-51-12064_ННИО_а
Foundation for the Development of Theoretical Physics and Mathematics BASIS 18-1-7-37-1
Ministry of Science and Higher Education of the Russian Federation 3.8515.2017/БЧ
The work of E. O. Burlakov was supported by the Russian Foundation for Basic Research (project Nos. 17-41-680975 and 18-31-00227) and the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS” (project No. 18-1-7-37-1). The work of E. S. Zhukovskiy was supported by the Russian Foundation for Basic Research (project Nos. 17-01-00553, 17-41-680975, and 17-51-12064) and the Ministry of Education and Science of the Russian Federation (project No. 3.8515.2017/БЧ).
Bibliographic databases:
Document Type: Article
UDC: 517.922, 517.927.4, 517.988
MSC: 55M20, 34A09, 34A12, 34A40, 34B15
Language: Russian
Citation: E. O. Burlakov, T. V. Zhukovskaya, E. S. Zhukovskiy, N. P. Puchkov, “Applications of covering mappings in the theory of implicit differential equations”, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part I, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 165, VINITI, Moscow, 2019, 21–33
Citation in format AMSBIB
\Bibitem{BurZhuZhu19}
\by E.~O.~Burlakov, T.~V.~Zhukovskaya, E.~S.~Zhukovskiy, N.~P.~Puchkov
\paper Applications of covering mappings in the theory of implicit differential equations
\inbook Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics".
Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part I
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 165
\pages 21--33
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into464}
\crossref{https://doi.org/10.36535/0233-6723-2019-165-21-33}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4030608}
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    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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