一类带有界回复力非线性Hill型方程的周期解

数学物理学报 ›› 2019, Vol. 39 ›› Issue (4): 761-772.

一类带有界回复力非线性Hill型方程的周期解

王超()

盐城师范学院数学与统计学院江苏盐城 224001

收稿日期:2018-01-15 出版日期:2019-08-26 发布日期:2019-09-11
作者简介:王超, E-mail:wangchaosudamath@163.com
基金资助:
国家自然科学基金(11571249);江苏省自然科学基金(BK20171275)

Periodic Solutions of a Class of Nonlinear Hill's Type Equations with Bounded Restoring Force

Chao Wang()

School of Mathematics and Statistics, YanCheng Teacher's University, Jiangsu Yancheng 224001

Received:2018-01-15 Online:2019-08-26 Published:2019-09-11
Supported by:
the NSFC(11571249);the Natural Science Fundation of Jiangsu Province(BK20171275)

摘要/Abstract

摘要：

该文研究了一类带有界回复力的Hill方程的周期解问题.针对权函数为正数的情形，证明了无穷多个次调和解的存在性.当权函数关于时间是偶函数时，证明了无穷多个偶次调和解的存在性和偶次调和解的稠密性分布.

关键词: Hill型方程, 权函数, 有界回复力, 次调和解, 对称周期解

Abstract:

In this pater, we study the existence and multiplicity of the periodic solutions of a class of Hill's type equations with bounded restoring force. We prove the existence of infinite of subharmonic solutions when the weight is positive. We also consider the existence, multiplicity and dense distribution of symmetric periodic solutions in case of even and periodic weight functions.

Key words: Hill's type equation, Weight functions, Bounded restoring force, Sub-harnomic solutions, Symmetric periodic solutions

中图分类号:

O175.14

王超. 一类带有界回复力非线性Hill型方程的周期解[J]. 数学物理学报, 2019, 39(4): 761-772.

Chao Wang. Periodic Solutions of a Class of Nonlinear Hill's Type Equations with Bounded Restoring Force[J]. Acta mathematica scientia,Series A, 2019, 39(4): 761-772.

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