@Article{CMR-33-2, author = {Xiumei, Xing and Ma, Jing and Lei, Jiao}, title = {Boundedness in Asymmetric Quasi-Periodic Oscillations}, journal = {Communications in Mathematical Research}, year = {2017}, volume = {33}, number = {2}, pages = {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. 

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2017.02.03}, url = {https://global-sci.com/article/81639/boundedness-in-asymmetric-quasi-periodic-oscillations} }