一类奇次微分系统极限环的存在性与惟一性  

Existence and uniqueness of limit cycles for a class of planar differential systems

作　　者：高静[1] 林京[1] 

机构地区：[1]合肥工业大学数学系,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2009年第4期588-590,共3页Journal of Hefei University of Technology：Natural Science

摘　　要：关于平面自治微分系统的定性研究,2次系统已有大量系统的结果,但是还没有得到完全解决,随着2次系统大量研究成果的产生,对3次系统研究工作也日益增多。文章对一类(2n+1)次微分系统进行了详细的讨论,主要运用G.Sansone定理及旋转向量场理论分析得出其极限环的存在性与惟一性及闭轨的完整结果,这是对3次系统研究成果的推广和延伸。3次系统的某些结论,在本文成为当n=1时的自然结论。This paper considers the （2n＋1）th differential systems. G. Sansone theorem and the theory of rotated vector fields are applied to discuss the existence and uniqueness of limit cycles for the planar differential systems. The existence, uniqueness and closed orbit of limit cycles are obtained, which are the extension of the results of the third differential system. Some results of the third differential system are the certain results as n=1.

关 键 词：平面微分系统 极限环 存在与惟一性 闭轨 

分 类 号：O175.1[理学—数学]