E-mail: kodani@auecc.aichi-edu.ac.jp
Abstract. In the paper, we give an existence theorem of periodic solution for Li\'enard 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 $\mu\not=0$. The result is an improvement of the author's previous estimation $\rho(\mu)<2.5425$.
AMSclassification. 34C05, 58F21
Keywords. van der Pol equation, limit cycle, amplitude