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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, Number 8, Pages 56–65
DOI: https://doi.org/10.26907/0021-3446-2021-8-56-65 (Mi ivm9703) 		 
This article is cited in 5 scientific papers (total in 5 papers)

On the solvability of a periodic problem for nonlinear ordinary differential equation of the second order

A. N. Naimova, M. M. Kobilzodab

a Vologda State University, 15 Lenin str., Vologda, 160000 Russia
b Russian-Tajik (Slavonic) University, 30 M. Tursun-zade str., Dushanbe, 734000 Republic of Tajikistan
Full-text PDF (327 kB) Citations (5)
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DOI: https://doi.org/10.26907/0021-3446-2021-8-56-65
Abstract: The article deals with a periodic problem for a nonlinear ordinary differential equation of the second order with the main positively homogeneous part selected. The paper uses the research scheme previously implemented by the authors in the study of the third two-point boundary value problem for a nonlinear ordinary differential equation of the second order. According to the research scheme, first in terms of the properties of the main positively homogeneous part, the conditions for a priori estimation of periodic solutions are found. And then in terms of a priori estimation theorems on the solvability of the periodic problem are formulated and proved using methods for calculating the rotation of vector fields. The results obtained can subsequently be generalized for systems of nonlinear ordinary differential equations of the second order.
Keywords: periodic problem, positive homogeneous function, a priori estimation, solvability of a periodic problem, rotation of a vector fields.
Received: 20.08.2020
Revised: 01.10.2020
Accepted: 24.12.2020
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2021, Volume 65, Issue 8, Pages 49–57
DOI: https://doi.org/10.3103/S1066369X21080065
Document Type: Article
UDC: 517.927
Language: Russian
Citation: A. N. Naimov, M. M. Kobilzoda, “On the solvability of a periodic problem for nonlinear ordinary differential equation of the second order”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 8, 56–65; Russian Math. (Iz. VUZ), 65:8 (2021), 49–57
Citation in format AMSBIB
\Bibitem{NaiKob21}
\by A.~N.~Naimov, M.~M.~Kobilzoda
\paper On the solvability of a periodic problem for nonlinear ordinary differential equation of the second order
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2021
\issue 8
\pages 56--65
\mathnet{http://mi.mathnet.ru/ivm9703}
\crossref{https://doi.org/10.26907/0021-3446-2021-8-56-65}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2021
\vol 65
\issue 8
\pages 49--57
\crossref{https://doi.org/10.3103/S1066369X21080065}
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    • This publication is cited in the following 5 articles:
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
     
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