In this paper, we consider the family of generalized Abel equations of the form

$$\begin{aligned} x'=A(t)x^m + B(t) x^n, \end{aligned}$$

where A, B are trigonometric polynomials and \(m,n\in \mathbb {N}\). We characterize the existence of non-trivial limit cycles in this family, in terms of the trigonometric monomials.

中文翻译：

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广义Abel方程非平凡极限环存在性的刻画。

在本文中，我们考虑以下形式的广义Abel方程族

$$ \ begin {aligned} x'= A（t）x ^ m + B（t）x ^ n，\ end {aligned} $$

其中A，  B是三角多项式，\（m，n \ in \ mathbb {N} \）。我们用三角单项式描述了这个家庭中非平凡极限环的存在。