Abstract

We study the existence of periodic solutions for a class of systems of first-order nonlinear ordinary differential equations on the plane. Using an a priori estimate of periodic solutions, we establish the homotopy invariance of the solvability property of the periodic problem, give a description of the homotopy classes, and prove a theorem about a necessary and sufficient condition for the solvability of the periodic problem.

中文翻译：

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平面上一类周期问题的可解性

摘要

我们研究平面上一类一阶非线性常微分方程组的周期解的存在性。使用对周期解的先验估计，我们建立了周期问题的可解性的同伦不变性，给出了同伦类的描述，并证明了关于周期问题的可解性的充要条件的一个定理。