一类奇性 $\phi$-Laplacian Rayleigh 型方程周期解的存在性

数学物理学报 ›› 2024, Vol. 44 ›› Issue (5): 1183-1193.

一类奇性 $\phi$-Laplacian Rayleigh 型方程周期解的存在性

钱玉婷¹,周学良²,程志波^1,^2,^*()

¹河南理工大学数学与信息科学学院河南焦作 454003
²新疆工业职业技术学院公共教学部乌鲁木齐 830022

收稿日期:2023-09-12 修回日期:2024-02-16 出版日期:2024-10-26 发布日期:2024-10-16
通讯作者: *程志波, E-mail: czb_1982@126.com
基金资助:
河南省高校科技创新人才项目(21HASTIT025);河南省自然科学基金(222300420449)

Existence of Periodic Solutions for $\phi$-Laplacian Rayleigh Equations with a Singularity

Qian Yuting¹,Zhou Xueliang²,Cheng Zhibo^1,^2,^*()

¹School of Mathematics and Information Science, Henan Polytechnic University, Henan Jiaozuo 454003
²Department of Public Education, Xinjiang Industrial Vocational and Technical College, Urumqi 830022

Received:2023-09-12 Revised:2024-02-16 Online:2024-10-26 Published:2024-10-16
Supported by:
Technological Innovation Talents in Universities and Colleges in Henan Province(21HASTIT025);Natural Science Foundation of Henan Province(222300420449)

摘要/Abstract

摘要：

该文考虑了一类 $\phi$-Laplacian Rayleigh 型方程, 其中非线性项在原点有奇性并且是非自治的. 通过应用 Mawhin 连续定理和一些分析方法, 证明了该方程在强排斥型奇性或强弱吸引型奇性条件下周期解的存在性.

关键词: 奇性, Rayleigh 方程, $\phi$-Laplacian 算子, 周期解

Abstract:

In this paper, we consider a class of $\phi$-Laplacian Rayleigh equation, where the nonlinear term is non-autonomous and has a singularity at the origin. By applications of Mawhin's continuation theorem and some analysis methods, we prove the existence of periodic solutions to the equation with a strong singularity of repulsive type (or weak and strong singularities of attractive type).

Key words: Singularity, Rayleigh equation, $\phi$-Laplacian, Periodic solution

中图分类号:

O175.1

钱玉婷, 周学良, 程志波. 一类奇性 $\phi$-Laplacian Rayleigh 型方程周期解的存在性[J]. 数学物理学报, 2024, 44(5): 1183-1193.

Qian Yuting, Zhou Xueliang, Cheng Zhibo. Existence of Periodic Solutions for $\phi$-Laplacian Rayleigh Equations with a Singularity[J]. Acta mathematica scientia,Series A, 2024, 44(5): 1183-1193.

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