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Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, Volume 7, Issue 2, Pages 277–288
DOI: https://doi.org/10.21638/11701/spbu01.2020.210 (Mi vspua189) 		 
This article is cited in 1 scientific paper (total in 1 paper)

IN MEMORIAM OF V. A. PLISS

On the existence of a solution of the boundary initial-value problem

V. V. Basov, Yu. A. Iljin

St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
Full-text PDF (581 kB) Citations (1)
DOI: https://doi.org/10.21638/11701/spbu01.2020.210
Abstract: An initial-value problem for an ordinary differential equation of the first order, is considered. It is supposed that the right-hand side of the equation is a continuous function defined on a set consisting of an open set and a part of its bound. Sufficient conditions of the existence and of non-existence of a solution through initial point belonging to the boundary part of the set of definition, are presented.
Keywords: initial-value boundary problem, existence of a solution, Peano segment.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00388
The work is supported by Russian Foundation for Basic Research (grant N 19-01-00388).
Received: 11.11.2019
Revised: 09.12.2019
Accepted: 12.12.2019
English version:
Vestnik St. Petersburg University, Mathematics, 2020, Volume 7, Issue 2, Pages 180–190
DOI: https://doi.org/10.1134/S1063454120020053
Document Type: Article
UDC: 517.911
MSC: 34A12
Language: Russian
Citation: V. V. Basov, Yu. A. Iljin, “On the existence of a solution of the boundary initial-value problem”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 7:2 (2020), 277–288; Vestn. St. Petersbg. Univ., Math., 7:2 (2020), 180–190
Citation in format AMSBIB
\Bibitem{BasIli20}
\by V.~V.~Basov, Yu.~A.~Iljin
\paper On the existence of a solution of the boundary initial-value problem
\jour Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
\yr 2020
\vol 7
\issue 2
\pages 277--288
\mathnet{http://mi.mathnet.ru/vspua189}
\crossref{https://doi.org/10.21638/11701/spbu01.2020.210}
\transl
\jour Vestn. St. Petersbg. Univ., Math.
\yr 2020
\vol 7
\issue 2
\pages 180--190
\crossref{https://doi.org/10.1134/S1063454120020053}
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