# On the existence of a conditionally periodic solution of one quasilinear differential system in the critical case

## DOI:

https://doi.org/10.26577/JMMCS-2018-4-553## Keywords:

conditionally periodic, accelerated convergence, frequency, resonance## Abstract

In the theory of nonlinear oscillations one often encounters conditionally periodic oscillations resulting from the superposition of several oscillations with frequencies incommensurable with each other. When finding a solution to a resonant quasilinear differential system in the form of a conditionally periodic function, the problem of a small denominator arises. Consequently, the proof of the existence, and even more the construction of such a solution is not an easy task. In this article, drawing on the work of VI. Arnold, I. Moser, and other researchers proved the existence and constructed a conditionally periodic solution of a second-order quasilinear differential system in the critical case. Accelerated convergence method by N.N. Bogolyubova, Yu.A. Mitropolsky, A.M. Samoylenko. The result can be applied to construct a conditionally periodic solution of specific differential systems.

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## How to Cite

*Journal of Mathematics, Mechanics and Computer Science*,

*100*(4), 8–17. https://doi.org/10.26577/JMMCS-2018-4-553