具有间隙的动力系统的极限环

The Limit Cycle of Dynamic System with Gaps

中文关键词:  Филиппов解  状态函数  特征点  极限环

英文关键词:Fillipov solution  state function  characteristic point  limit cycle.

中文摘要:

      本文研究了系统ｘ＋ｆ（ｘ）＋ｇ（ｘ）＝０的极限环的存在性，其中ｇ（ｘ）有两个间断点并且不满足ｇ（ｘ）·ｘ＞０（ｘ≠０）．还引进［２，３］中定义的Филиппов解的概念，利用Филиппов解的整体存在性和普遍唯一性定理解决方程的解的存在唯一性问题，得到了几个极限环存在性定理

英文摘要:

      This work is about the existence of the limit cycle of equation ｘ＋ｆ（ｘ）＋ｇ（ｘ）＝０, where g(x) has two discontinuous points and does not satisfy g(x)·x>0,x≠0 . We use the concept of Fillipov solution defined in 4,5 and get several theorems of existence of limit cycle.