【摘要】 <正> 本文也来研究Liénard方程(1)的零解的全局稳定性(方程(1)中假设f(x),g(x)是连续可微函数)。本文所得的结果与文[1]中的例4中所得结果相比较不仅减弱了条件,并且证明更简明。我们开始证明之前先,先介绍将在证明中所用到的定理。 考虑系统更多还原

【Abstract】 We consider global asymptotic stability of the trivial solution of Lienard’s equationx + f(x)z + g(x) =0, g(0)=0. (1)Instead of (1) we will discuss the equivalent system(2)We obtain the following resultTheorem The trivial solution of system (2) is globally asymptotically stable if f(x) and g(x) satisfy the following conditions a) xg(x)>0 for all x≠0,b)c)In comparison with example 2[1,ex、4], we obtain result with a weaker assumption on f(x) and a simpler proof.更多还原