一类扰动系统极限环个数的最小上界

On the least upper bound of the number of limit cycles of a class perturbed system

讨论了一类扰动系统的弱化 Hilbert第 1 6问题 ,在其一阶 Melnicov函数不恒等于零的情况下 ,得到了该系统的极限环个数最小上界的完整结论 .作为应用 ,还给出了两个具体的例子 .

In this paper, the weakened Hilbert 16 th problem of class perturbed system are discussed. For this system, if M 1(h)0, we get an integated conclusion of the least upped bound of the number of limit cycles of this system. By way of an application, we also give two idiographic examples.