一类具有偏差变元的p-Laplacian Liénard型方程在吸引奇性条件下周期解的存在性

数学物理学报 ›› 2019, Vol. 39 ›› Issue (2): 277-285.

一类具有偏差变元的p-Laplacian Liénard型方程在吸引奇性条件下周期解的存在性

程志波^1,²,毕中华¹,姚绍文^1,*()

¹ 河南理工大学数学与信息科学学院河南焦作 454003
² 四川大学数学学院成都 610064

收稿日期:2017-11-09 出版日期:2019-04-26 发布日期:2019-05-05
通讯作者: 姚绍文 E-mail:yaoshaowen@hpu.edu.com
基金资助:
国家自然科学基金(11501170);国家自然科学基金(71601072);中国博士后基金(2016M590886);河南省高校基本科研业务费专项资金(NSFRF170302);河南理工大学博士基金(B2013-055)

Periodic Solution for p-Laplacian Liénard Equation with Attractive Singularity and Time-Dependent Deviating Argument

Zhibo Cheng^1,²,Zhonghua Bi¹,Shaowen Yao^1,*()

¹ School of Mathematics and Information Science, Henan Polytechnic University, Henan Jiaozuo 454003
² Department of Mathematics, Sichuan University, Chengdu 610064

Received:2017-11-09 Online:2019-04-26 Published:2019-05-05
Contact: Shaowen Yao E-mail:yaoshaowen@hpu.edu.com
Supported by:
the NSFC(11501170);the NSFC(71601072);the China Postdoctoral Science Foundation(2016M590886);the Fundamental Research Funds for the Universities of Henan Provience(NSFRF170302);the Henan Polytechnic University Doctor Fund(B2013-055)

摘要/Abstract

摘要：

该文考虑了一类具有偏差变元的奇性$p$-Laplacian Liénard型方程

$ (\varphi_p(x'(t)))'+f(x(t))x'(t)+g(t, x(t-\sigma(t)))=e(t), $

其中$g(x)$在原点处具有吸引奇性.通过应用Manásevich-Mawhin连续定理和一些分析方法,证明了这个方程周期解的存在性.

关键词: Liénard型方程, 周期解, 吸引奇性, p-Laplacian, 偏差变元

Abstract:

In this paper, we consider a kind of $p$-Laplacian singular Liénard equation with time-dependent deviating argument

$(\varphi_p(x'(t)))'+f(x(t))x'(t)+g(t, x(t-\sigma(t)))=e(t), $

where $g$ has a attractive singularity at $x=0$. By applications of Manásevich-Mawhin continuation theorem and some analysis skills, sufficient conditions for the existence of periodic solution is established.

Key words: Liénard equation, Periodic solution, Attractive singularity, p-Laplacian, Time-dependent deviating argument

中图分类号:

O175.12

程志波,毕中华,姚绍文. 一类具有偏差变元的p-Laplacian Liénard型方程在吸引奇性条件下周期解的存在性[J]. 数学物理学报, 2019, 39(2): 277-285.

Zhibo Cheng,Zhonghua Bi,Shaowen Yao. Periodic Solution for p-Laplacian Liénard Equation with Attractive Singularity and Time-Dependent Deviating Argument[J]. Acta mathematica scientia,Series A, 2019, 39(2): 277-285.

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