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ON A PRIORI ESTIMATE OF PERIODIC SOLUTIONS OF THE SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS OF THE SECOND ORDER WITH THE MAIN POSITIVELY HOMOGENEOUS NONLINEARITY
- Authors: Mukhamadiev E.1, Naimov A.N1
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Affiliations:
- Vologda State University
- Issue: Vol 61, No 2 (2025)
- Pages: 200-206
- Section: ORDINARY DIFFERENTIAL EQUATIONS
- URL: https://journal-vniispk.ru/0374-0641/article/view/299125
- DOI: https://doi.org/10.31857/S0374064125020058
- EDN: https://elibrary.ru/HWWJHO
- ID: 299125
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Abstract
For the system of ordinary differential equations of the second order with the main positively homogeneous nonlinearity, an a priori estimate of periodic solutions of a fixed period is investigated. New conditions of a priori estimate are found, in which the influence of the properties of the main nonlinear part, including its set of zeros, is mediated by functional estimates from above and below. The feasibility of the new conditions is investigated for three types of nonlinearities.
About the authors
E. Mukhamadiev
Vologda State University
Email: emuhamadiev@rambler.ru
Russia
A. N Naimov
Vologda State University
Email: naimovan@vogu35.ru
Russia
References
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- Naimov, A.N. and Khakimov, R.I., Estimation of derivatives of periodic solutions of one class of systems of nonlinear ordinary differential equations of the second order, Vestnik Tadzhikskogo natsional’nogo universiteta. Seriya yestestvennykh nauk, 2017, no. 1/5, pp. 12–16.
- Mukhamadiev, E. and Naimov, A.N., On the solvability of a periodic problem for a system of non-linear ordinary differential equations of second order, Differ. Equat., 2024, vol. 60, no. 3, pp. 286–295.
- Mukhamadiev, E. and Naimov, A.N., On the solvability of a periodic problem for a two-dimensional system of ordinary differential equations of the second order, Differ. Equat. Contr. Process., 2024, no. 2, pp. 46–58.
- Naimov, A.N., On the number of nonstationary bounded trajectories of a class of autonomous systems on the plane, Differ. Equat., 2008, vol. 44, no. 8, pp. 1082–1087.
- Mukhamadiev, E. and Naimov, A.N., On a priori estimate and the existence of periodic solutions for a class of systems of nonlinear ordinary differential equations, Russ. Math., 2022, vol. 66, no. 4, pp. 32–42.
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