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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2024, Number 8, Pages 45–54
DOI: https://doi.org/10.26907/0021-3446-2024-8-45-54
(Mi ivm10005)
 

On a priori estimate of periodic solutions of a system of nonlinear ordinary differential equations of the second order

E. Muhamadiev, A. N. Naimov

Vologda State University, 15 Lenin str., Vologda, 160000 Russia
References:
Abstract: The question of a priori estimation of periodic solutions for a system of non-linear ordinary differential equations of the second order with a distinguished main positively homogeneous part is investigated. In this question, the well-known methods for deriving an a priori estimation of periodic solutions for similar systems of first-order ordinary differential equations are not directly applicable. Combining these methods with the idea of qualitative research of singularly perturbed ordinary differential equations, conditions are found that provide an a priori estimation of periodic solutions for the system of second-order equations. The conditions for the a priori estimation are formulated in terms of the properties of the main positively homogeneous part of the system of equations. The existence of periodic solutions is proved to be invariant under a continuous change of the main positively homogeneous part and the conditions of a priori estimation are preserved. Based on the results obtained, in the future, it is possible to investigate the existence of periodic solutions.
Keywords: main positively homogeneous part, perturbation, periodic solution, a priori estimation, invariance of the existence of periodic solutions.
Funding agency Grant number
Russian Science Foundation 23-21-00032
Исследование выполнено за счет гранта Российского научного фонда № 23-21-00032, https://rscf.ru/project/23-21-00032/.
Received: 10.09.2023
Revised: 10.09.2023
Accepted: 26.12.2023
Document Type: Article
UDC: 517.927.4
Language: Russian
Citation: E. Muhamadiev, A. N. Naimov, “On a priori estimate of periodic solutions of a system of nonlinear ordinary differential equations of the second order”, Izv. Vyssh. Uchebn. Zaved. Mat., 2024, no. 8, 45–54
Citation in format AMSBIB
\Bibitem{MuhNai24}
\by E.~Muhamadiev, A.~N.~Naimov
\paper On a priori estimate of periodic solutions of a system of nonlinear ordinary differential equations of the second order
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2024
\issue 8
\pages 45--54
\mathnet{http://mi.mathnet.ru/ivm10005}
\crossref{https://doi.org/10.26907/0021-3446-2024-8-45-54}
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    Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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