华东师范大学学报(自然科学版) ›› 2004, Vol. 2004 ›› Issue (3): 1-5，28.

• 数学 统计学 •    下一篇

非线性方程极限环的存在唯一性

刘兴波   

  1. 华东师范大学 数学系，上海 200062
  • 收稿日期:2003-03-14 修回日期:2003-06-18 出版日期:2004-09-25 发布日期:2004-09-25
  • 通讯作者: 刘兴波

Existence and Uniqueness of Limit Cycle for A Nonlinear Equation

LIU Xing-bo   

  1. Department of Mathematics, East China Normal University, Shanghai 200062， China
  • Received:2003-03-14 Revised:2003-06-18 Online:2004-09-25 Published:2004-09-25
  • Contact: LIU Xing-bo

摘要： 讨论平面自治系统x=Q(x,y), y=P(x)的极限环的存在唯一性，简化了文献［7~9］中极限环存在性条件，并进一步论证了其极限环唯一性，用较简洁直观的方法，得到系统存在唯一极限环的一组条件.

关键词: 极限环, 存在性, 唯一性, 极限环, 存在性, 唯一性

Abstract: This paper considers the existence and uniqueness of limit cycle for a planar autonomous system x=Q(x,y), y=P(x). The conditions of existence of limit cycle in papers ［7~9］ are simplified, in addition, The uniqueness of limit cycle is discussed. Simpler conditions for the existence and uniqueness of limit cycle are obtained.

Key words: existence, uniqueness, limit cycle, existence, uniqueness

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