| Liénard方程至多存在n个极限环的充分条件 |
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| 引用本文： | 陈秀东,陈勇. Liénard方程至多存在n个极限环的充分条件[J]. 数学研究及应用, 2003, 23(2): 333-338 |
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| 作者姓名： | 陈秀东 陈勇 |
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| 作者单位： | 大连理工大学应用数学系,辽宁,大连,116024 |
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| 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.
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| 关 键 词： | 极限环 状态函数 |
| 文章编号： | 1000-341X(2003)02-0333-06 |
| 收稿时间： | 2001-02-07 |
| 修稿时间： | 2001-02-07 |
A Sufficient Condition for Lienard''s Equation Existing at Most n Limit Cycles |
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| CHEN Xiu-dong and CHEN Yong. A Sufficient Condition for Lienard''s Equation Existing at Most n Limit Cycles[J]. Journal of Mathematical Research with Applications, 2003, 23(2): 333-338 |
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| Authors: | CHEN Xiu-dong and CHEN Yong |
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| Affiliation: | Dept. of Appl. Math.; Dalian University of Technology; Liaoning; China;Dept. of Appl. Math.; Dalian University of Technology; Liaoning; China |
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| Abstract: | 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. |
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| Keywords: | limit cycle state function |
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