一类奇次微分系统的极限环的存在性

The existence of limit cycles of degree (2n+1) for differential systems

对奇次微分系统·ｘ＝ － ｙ＋ δｘ＋ ａｘｙ＋ ｂｘ２ｎ＋１ ，·ｙ＝ ｘ 进行定性分析，运用Ｎ．Ｌｅｖｉｓｏｎ，Ｏ．Ｋ．Ｓｍｉｔｈ 定理和А．В．Драгидёв定理得到其在一定条件下极限环的存在性，并借助对称方法、特殊曲线以及构造Ｄｕｌａｃ

The differential system =-y+δx+axy+bx 2n+1 ,=x is studied.We get two existence theorems of limit cycles of the system by applying N.Levison,O.K.Smith Theorem and A.B.Драгидёв Theorem,and two nonexistence theorems of limit cycles by the symmetry method,special curve and Dulac function method.