Year: 2017
Author: Xiumei Xing, Jing Ma, Lei Jiao
Communications in Mathematical Research , Vol. 33 (2017), Iss. 2 : pp. 121–128
Abstract
In the paper, by applying the method of main integration, we show the boundedness of the quasi-periodic second order differential equation $x′′+ax^+−bx^−+ ϕ(x) = p(t)$, where $a ≠ b$ are two positive constants and $ϕ(s)$, $p(t)$ are real analytic functions. Moreover, the $p(t)$ is quasi-periodic coefficient, whose frequency vectors are Diophantine. The results we obtained also imply that, under some conditions, the quasi-periodic oscillator has the Lagrange stability.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.13447/j.1674-5647.2017.02.03
Communications in Mathematical Research , Vol. 33 (2017), Iss. 2 : pp. 121–128
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 8
Keywords: boundedness quasi-periodic KAM theorem