一类以拋物线为特殊积分曲线的二次系统存在极限环的必要条件

THE NECESSARY CONDITION FOR THE EXISTENCE OF THE LIMIT CYCLES OF A KIND OF THE QUADRATIC DIFFERENTIAL SYSTEMS WITH A PARABOLIC THE SPCEICAL MTEGRAL CURVE

本文将一类以抛物线为特殊积分曲线的二次系统分成四种情形来研究,分别给出了存在极限环的必要条件和易于判别极限环不存在的充分条件。

For a kind of the quadratic differential systems with a parabolic the spceical integral curve, we classify it into four cirumstances, then we have obtained the necessary conditions for the existence of the limit cycles and a group of the sufficiten conditions for discriminating the unexistence of limit cycles in diffenent cases.