Liénard方程极限环的存在性

On the Existence of Limit Cycles of Lienard Equation

本文在没有常设条件G(±∞)=+∞的情况下,证明了Linard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”.

In this paper, we have proved several theorems which guarantee that the Lienard equation has at least one or n limit cycles without using the traditional assumption G(±∞) = + ∞. Thus some results in [3-5] are extended. The limit cycles can be 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 ontained in each other'.