关于具有二阶细焦点的二次系统

On quadratic differential system with a weak focus of 2 order

研究了具有二阶细焦点的二次系统的极限环存在性的某些问题.首先,简化了一个极限环存在性定理的证明,然后证明了若L满足不等式ψ1(-1 (L+1))>ψ2(-1 (L+1)),则二次系统(E2)在原点O外围至多存在一个极限环的定理,并猜测当L0<L<-0.705602时,结论依然成立.

It is studied some problems of existences of limit cycle. First gives a brif proof of existences of limit cycle, then proves a theorem that if L satisfies inequation ψ1(-1/(L+1))>ψ2(-1/(L+1)), then there is a limit cycle at most in quadratic system outside zero. Further more gives a subjection that when L0<L<-0.705?602, the above conclusion holds.