Liénard方程至多存在n个极限环的充分条件

A Sufficient Condition for Lienard's Equation Existing at Most n Limit Cycles

中文关键词:  极限环  状态函数

英文关键词:limit cycle  state function

中文摘要:

      在文[7,8]中对Lienard方程提出状态函数的概念.本文我们将极限环存在性的研究转化为微积分中连续函数(状态函数)零点的研究,给出了Lienard方程至多存在n个极限环的充分条件.最后证明了A.Lins,W.de Melo,C.C.Pugh的猜想.

英文摘要:

      In this paper, based on the concept of state function [7,8], the study of limit cycle existence is transformed to the study of zero points of continuous function. As a result, we obtain a sufficient condition for Lienard's equation existing at most n limit cycles and give an affirmative answer to Lins, A. , W. de Melo and C. C. Pugh's conjecture.