一类广义Liénard型系统的解的有界性

Boundedness of Solutions for a Class of Generalized Liénard type System

研究具有多个奇点的广义Ｌｉéｎａｒｄ 系统ｘ＝ １ａ（ｘ）（ｈ（ｙ）－ Ｆ（ｘ）），ｙ＝ － ａ（ｘ）ｇ（ｘ）解的有界性， 获得了系统解正向有界的充要条件， 进而得全局渐近稳定的充要条件。

The boundedness of the solutions for the generalized Liénard type system (E):=1a(x)[h(y)-F(x)],=-a(x)g(x) with a finite or infinite number of singular points are dealed with, and some sufficient and necessary conditions for all solution of the system to be bounded for t≥0 are given. Moreover, the necessary and sufficient condition for the global asymptotic stability for (E) are obtained.