一类带有界回复力非线性Hill型方程的周期解  

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

作　　者：王超 Wang Chao(School of Mathematics and Statistics, YanCheng Teacher's University,Jiangsu Yancheng 224001)

机构地区：[1]盐城师范学院数学与统计学院

出　　处：《数学物理学报（A辑）》2019年第4期761-772,共12页Acta Mathematica Scientia

基　　金：国家自然科学基金(11571249);江苏省自然科学基金(BK20171275)~~

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.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.

关 键 词：Hill型方程 权函数 有界回复力 次调和解 对称周期解 

分 类 号：O175.14[理学—数学]