On the existence of a periodic solution of the Liénard system
DOI:
https://doi.org/10.24193/subbmath.2021.1.04Keywords:
Liénard system, a periodic solution.Abstract
The Li\'{e}nard system $\frac{dx}{dt}=y,\quad \frac{dy}{dt}=-f(x)y-g(x)$ is considered.Under some assumptions on functions $f(x)$ and $g(x)$, we estimate the domain of location of the unique stable limit cycle of the Li\'{e}nard system.This estimation has the form $\alpha_2<x<\alpha_1$, where $\alpha_1$ and $\alpha_2$ are respectively the positive the negative roots of the equation $\int_0^{\alpha}\left[\int_0^xf(s)ds\right] g(x)dx=0$.
Mathematics Subject Classification (2010): 34C05, 34C07, 34C25, 34C15, 34A26.
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