Liénard方程极限环的存在性

本文在没有常设条件G(±∞)=+∞的情况下,证明了Liénard方程存在极限环的几个充分性定理,推广了文[3～6]的某些结果.这些定理给出的条件均可估计极限环的存在区域.至少在n个极限环的充分性定理3、4的条件既不要求F(x)是奇函数,也不要求F(x)"n重互相相容"或"n重互相包含".     

ON THE EXISTENCE OF LIMIT CYCLES OF LIENARD EQUATION

In this paper,we have proved several theorems which guarantee that the Lienardequation has at least one or n limit cycles without using the traditional assmuption G(±∞)= ∞.Thus some results in[3 -5]are extended.The limit cycles can be located by ourtheorems.Theorems3 and4 give sufficient conditions for the existence of n limit cycleshaving no need of the conditions that the function F(x)is odd or“nth order compatible witheach other”or“nth order contained in each other”.     

On the existence of limit cycles of Liénard equation

In this paper, we have proved several theorems which guarantee that the Liénard equation has at least one or n limit cycles without using the traditional assmuption G(±) =+. Thus some results in [3–5] are extended. The limit cycles can he located by our theorems. Theorems 3 and 4 give sufficient conditions for the existence of n limit cycles having no need of the conditions that the function F(x) is odd or nth order compatible with each other or nth order contained in each other.