中文摘要：

研究了一类三次退化中心的极限环分支问题.通过计算一阶Melnikov函数,得到了退化中心的周期环域在任意小扰动下分支出极限环的个数.

英文摘要：

In this paper, we deal with the bifurcation problem of limit cycles of a class of cubic degenerate centers. By computing the first order Melnikov function, we obtain that the number of limit cycles bifurcating from the period annulus of the cubic degenerate centers.