第二类Abel方程的变号周期解
Periodic solutions with nonconstant sign in Abel equations of the second kind
摘要：
第二类Abel方程的常号周期解的研究可以通过第一类方程来进行。这是因为在变换$x\mapsto x^{-1}$下情况是等价的，并且在文献中有许多关于第一类方程的结果。然而，当人们寻求具有非常数符号的解时，等价性就被打破了。本文研究第二类Abel方程的非常号周期解。具体地说，我们得到了充分条件，以确保存在一个周期解，共享的首项系数的阿贝尔方程的零点。研究了这类解的唯一性和稳定性。
英文摘要：
The study of periodic solutions with constant sign in the Abel equation of the second kind can be made through the equation of the first kind. This is because the situation is equivalent under the transformation $x\mapsto x^{-1}$, and there are many results available in the literature for the first kind equation. However, the equivalence breaks down when one seeks for solutions with nonconstant sign. This note is devoted to periodic solutions with nonconstant sign in Abel equations of the second kind. Specifically, we obtain sufficient conditions to ensure the existence of a periodic solution that shares the zeros of the leading coefficient of the Abel equation. Uniqueness and stability features of such solutions are also studied.
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