关于广义Liénard系统的正半轨线与特征曲线相交的充要条件

The sufficient and necessary conditions of the generalized Liénard system for intersection of positive semiorbits with characteristic curve

讨论了一类广义Liénard系统的问题.获得了广义Liénard系统 x = h(y) - F(x), y =- g(x)p(y)过平面上任意一点的正半轨线与特征曲线 h(y) = F(x) 相交的充要条件,所得结果推广和改善了此类广义Liénard 系统的结果.

This paper deals with the problem of the generalized Liénard. It shows that some sufficient and necessary conditions of the generalized Liénard system =h(y)-F(x),=-g(x)p(y) for intersection of positive semiorbits with characteristic curve h(y)=F(x) through any point on the plane can be obtained. The results of the generalized Liénard system are extended and imporved.