广义Liénard系统零解全局渐近稳定的充要条件

THE SUFFICIENT AND NECESSARY CONDITIONSFOR GLOBAL ASYMPTOTIC STABILITY OF THE TRIVIALSOLUTION FOR GENERALIZED Liénards SYSTEMS

研究了广义Ｌｉéｎａｒｄ系统ｄｘｄｔ＝１ａ（ｘ）［ｈ（ｙ）－Ｆ（ｘ）］，ｄｙｄｔ＝－ａ（ｘ）ｇ（ｘ）零解的全局渐近稳定性问题，得到了在一定条件下保证此系统零解为全局渐近稳定的充要条件，推广和改进了许多已知结果．

This paper studies the global asymptotic stability of the trivial solution of generalized Liénards systemdydt=-a(x)g(x)through constructing new Liapunov function. The sufficient and necessary conditions for global asymptotic stability under given conditions are obtained and many known results are improved and extended.