On the uniqueness of periodic solutions for a Rayleigh–Liénard system with impulses

IF 1.3 2区数学 Q1 MATHEMATICS

Mathematische Annalen Pub Date : 2024-09-17 DOI:10.1007/s00208-024-02996-5

Hebai Chen, Jie Jin, Zhaoxia Wang, Dongmei Xiao

引用次数: 0

Abstract

This paper is to provide a criterion of the uniqueness of periodic solutions for a Rayleigh-Liénard system with state-dependent impulses. Notice that such results of a planar system with state-dependent impulses are few. Moreover, the Rayleigh-Liénard system with state-dependent impulses has wide applications, such as a simple pendulum and a spring vibrator. Further, we obtain the uniqueness of periodic solutions of the simple pendulum with state-dependent impulses and the spring vibrator with state-dependent impulses by the criterion.

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论带脉冲的 Rayleigh-Liénard 系统周期解的唯一性

本文旨在为具有状态相关脉冲的 Rayleigh-Liénard 系统提供周期解的唯一性准则。我们注意到，具有状态相关脉冲的平面系统的此类结果很少。此外，与状态相关脉冲的雷利-李纳系统应用广泛，如简单摆和弹簧振动器。此外，我们还通过判据得到了具有状态相关脉冲的简摆和具有状态相关脉冲的弹簧振子的周期解的唯一性。

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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来源期刊

Mathematische Annalen 数学-数学

CiteScore

2.90

自引率

7.10%

发文量

181

审稿时长

4-8 weeks

期刊介绍： Begründet 1868 durch Alfred Clebsch und Carl Neumann. Fortgeführt durch Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück und Nigel Hitchin. The journal Mathematische Annalen was founded in 1868 by Alfred Clebsch and Carl Neumann. It was continued by Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguigon, Wolfgang Lück and Nigel Hitchin. Since 1868 the name Mathematische Annalen stands for a long tradition and high quality in the publication of mathematical research articles. Mathematische Annalen is designed not as a specialized journal but covers a wide spectrum of modern mathematics.