【摘要】 本文研究系统证明了当d=0时无极限环.当d≠0时,不失一般性可设E=F=d=1,也得到颇为宽广的无环性条件.所用的方法都是作Dulac函数.当这些条件不成立时,作变换将上一系统化为二次系统由此直接得出在原点邻近存在唯一极限环的局部性条件.更多还原

【Abstract】 This paper studies the following system of equationsIt is proved that for the case d=0 there is no limit cycle. When d≠0 there is no lose of generality. If it is assumed that E=F=d=1, and hence rather wide conditions for the nonexistence of limit cycles are obtained. All the methods make use of seme Dulac functions. When these conditions do not hold true, the system can be changed into the following quadric system. Then the looal condition for the existenoe of the only limit oyole near the origin can be directly obtained.更多还原