方程x＝e^y－1－F（x），y＝－yg（x）的极限环的存在性

Existence Of Limit Cycles Of Equation x=e￣y-1-F(x),y=--yg(x)

对方ｘ＝（ｙ）＝Ｆ（ｘ），ｙ＝－ｇ（ｘ）的研究已经很多．不过以往的研究都假设（±∞）＝±∞，本文讨论了下面一类方程ｘ＝ｅ￣ｙ－１－Ｆ（ｘ），ｙ＝－ｙｇ（ｘ）的极限环的存在性问题。给出了此类方在存在极限环，不存在极限环与至多有一个极限环的充分条件。

There have been a lot of studies to the equation x=(y)-F(x),y=-g(x),but the study before all stipposed (±∞)=±∞, In this paper,we give up this conditionand argue the question of existence of limit cycles of equation x=e￣y-1-F(x),y=-yg(x).The stifficient conditions for the existence and nonexistence of limit cycles and at most a limitcycle for this kind of equation are obtained.