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van der Pol equation; limit cycle; amplitude
In the paper, we give an existence theorem of periodic solution for Liénard equation $\dot{x}=y-F(x)$, $\dot{y}=-g(x)$. As a result, we estimate the amplitude $\rho (\mu )$ (maximal $x$-value) of the limit cycle of the van der Pol equation $\dot{x}=y-\mu (x^3/3-x)$, $\dot{y}=-x$ from above by $\rho (\mu )<2.3439$ for every $\mu \ne 0$. The result is an improvement of the author’s previous estimation $\rho (\mu )<2.5425$.
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