Open AccessON THE EXISTENCE OF A CONDITIONALLY PERIODIC SOLUTION OF A QUASILINEAR SYSTEM DIFFERENTIAL EQUATION IN THE CRITICAL CASE
Author(s) -
Zh. Suleimenov,
S.K. Kuanysh
Publication year - 2020
Publication title -
habaršy. fizika-matematika seriâsy
Language(s) - English
Resource type - Journals
ISSN - 1728-7901
DOI - 10.51889/2020-4.1728-7901.08
Subject(s) - mathematics , superposition principle , mathematical analysis , function (biology) , differential equation , convergence (economics) , nonlinear system , differential (mechanical device) , order (exchange) , physics , quantum mechanics , finance , evolutionary biology , economics , biology , economic growth , thermodynamics
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 V.I. 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.