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

Вестник КазНУ. Серия математика, механика, информатика

Zh. Suleimenov¹ 

[1] Al-Farabi Kazakh National University;

关键词: conditionally periodic;    accelerated convergence;    frequency;    resonance;   

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

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown