(Ⅲ)_(m=0)类二次系统的极限环问题(Ⅰ)(英文)

LIMIT CYCLE PROBLEM FOR THE QUADRATIC SYSTEM OF TYPE (Ⅲ)_(m=0), (Ⅰ)

从本文开始我们对(Ⅲ)m=0类二次系统的极限环问题作了一系统研究,按照其系数的各种不同情况分类讨论．本文考察l<1/2,0<n<1和l<0,n>1的情况,给出了极限环惟一性的一些结论,并指出有时在一个焦点外围可以存在两个极限环,同时分析了系统的拓扑结构的变化．

Starting from this paper, we will give a systematic study for the limit cycle problem of the quadratic system of type （Ⅲ）m=0. There are many different cases for 1 the coefficients of the system, in which two typical cases with l 〈1/2,0 〈 n 〈 1 and l〈 0, n 〉 1 are considered here. Some results on the uniqueness of limit cycles are obtained. We also point out that there are two limit cycles around a focus under certain conditions connected with some global analysis for the system.