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

IF 0.8 4区数学 Q2 MATHEMATICS

Differential Equations Pub Date : 2024-09-11 DOI:10.1134/s0012266124050112

A. N. Naimov, M. V. Bystretsky

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引用次数: 0

摘要

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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On the Existence of Periodic Solutions of a System of Second-Order Ordinary Differential Equations with a Quasihomogeneous Nonlinearity

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.

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来源期刊

Differential Equations 数学-数学

CiteScore

1.30

自引率

33.30%

发文量

审稿时长

3-8 weeks

期刊介绍： Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.