广义Lienard系统的半轨趋向无穷的条件

A Condition for the Half-Orbit of a Generalized Lienard System Approaching Infinity

给出了广义Lienard系统.x=h(y)-F(x),.y=-g(x)的正(负)半轨不震荡而趋向无穷的充分条件,文献:"广义Lienard系统的全局中心"中的定理可以作为它的推论。文中的结论对研究Lienard系统解的震荡性,稳定性也是有用的。

In this paper,a sufficient condition is given for the positive（negative） half-orbit of the generalized Lienard system =h（y）-F（x）,=-g（x） non-oscillation but approaching infinity.The theorem of On the Centers of Generalized Lienard System can be used as an inference of it.The result in this paper is also useful to studying the oscillation and the stability of Lienard systems.