On the Existence of Periodic Solutions of a System of Second-Order Ordinary Differential Equations with a Quasihomogeneous Nonlinearity
Pub Date : 2024-09-11
DOI:10.1134/s0012266124050112
引用次数: 0
Abstract
In the present paper, we study an a priori estimate and the existence of periodic solutions of a given period for a system of second-order ordinary differential equations with the main quasihomogeneous nonlinearity. It is proved that an a priori estimate of periodic solutions takes place if the corresponding unperturbed system does not have nonzero bounded solutions. Under the conditions of the a priori estimate, using methods for calculating the mapping degree of vector fields, a criterion for the existence of periodic solutions is stated and proved for any perturbation in a given class. The results obtained differ from earlier results in that the set of zeros of the main nonlinearity is not taken into account.
论具有准均质非线性的二阶常微分方程系统周期解的存在性
摘要 本文研究了具有主齐次非线性的二阶常微分方程系统的先验估计和给定周期的周期解的存在性。研究证明，如果相应的未扰动系统不存在非零有界解，周期解的先验估计就会发生。在先验估计的条件下，利用计算向量场映射度的方法，针对给定类别中的任何扰动，阐述并证明了周期解存在的标准。所获得的结果与之前的结果不同，因为它没有考虑主非线性的零点集。
本文章由计算机程序翻译，如有差异，请以英文原文为准。
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