Lienard方程存在唯一、稳定周期解的一个充分条件

本文给出了在下列条件下:1) f(x)∈C~0(-∞,∞);f(x)是偶函数;f(0) <0;2) F(x)=(?)f(t)dt;F(x)=0有唯一的正实根 x=a;0a 时F(x)>0且为单调不减函数;3) g(x)∈C~0(-∞,∞);g(x)是奇函数,且满足 Lipschitz 条件;xg(x)>0,x≠04) F(+∞)>+∞;G(+∞)<+∞;其中 G(x)=(?)g(t)dt 方程(?)+f(x)(?)+g(x)=0存在唯一稳定周期解的一个充分条件.

A SUFFICIENT CONDITION FOR STABLE AND UNIQUE PERIODIC SOLUTION OF LIENARD EQUATION (?)+f(x)(?)+g(x)=0

In this paper,a sufficient condition for stable and unique periodic solution of lienard equation is given by using qualitative method of differential equations.