非线性方程极限环的存在性

<正> 关于 Liénard 型方程(dx)/(dt)=y-F(x),(dy)/(dt)=-g(x)的极限环的存在性,已有很多工作.但对一般的非线性方程(?)有关的结果却还不多见.本文给出方程(1)存在极限环的一个充分性准则,所要求的条件比[3]的条件稍弱.同时把 Neumann 关于 Liénard 型方程极限环的个数、位置的有关结果推广到方程(1)的情况.对于更一般的非线性方程     

A Discussion on the Existence of Limit Cycle of Equations =P(y),=Q(x,y)

For the system of differential equations having the form (?)=P(y),(?)=Q(x,y), (1) R.M. Cooper has given an analytic criterion for the existence of limit cycle. [1] In which p: R~1→R~1 and Q: R~2→R~1 are everywhere continuous and locally Lipschitzian, Q_y(x,y) is continuous at (0,0) and is defined for all (x,y). His result is as follows: