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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
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.
Received: 11.11.2019 Revised: 09.12.2019 Accepted: 12.12.2019
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
Linking options:
https://www.mathnet.ru/eng/vspua189 https://www.mathnet.ru/eng/vspua/v7/i2/p277
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