一类带有逐段常变量的二阶微分方程的概周期解  

Almost Periodic Solutions on a Class Second-order Differential Equations with Piecewise Constant Argument

作　　者：姚慧丽 张悦娇 侯盛楠 YAO Hui-li;ZHANG Yue-jiao;HOU Sheng-nan(School of Applied Sciences,Harbin University of Science and Technology,Harbin 150080,China)

机构地区：[1]哈尔滨理工大学理学院

出　　处：《哈尔滨理工大学学报》2019年第3期143-148,共6页Journal of Harbin University of Science and Technology

基　　金：黑龙江省教育厅科学技术研究项目(12511110)

摘　　要：基于微分方程的概周期解比周期解更具有一般性,本文将对一类带有逐段常变量的二阶微分方程的概周期解进行研究。根据这类方程的解在整数点的连续性,构造了一类非齐次差分方程。利用对应的齐次差分方程的特征根,并借助于相应的差分方程的概周期序列解和概周期函数以及概周期序列的一些性质,探讨了这类方程的概周期解的存在性以及该类解的唯一性。Almost periodic solutions of differential equations are more general than periodic solutions,so almost periodic solutions will be studied on a class second-order differential equations with piecewise constant argument.A class of nonhomogeneous difference equations are constructed by the continuity of solutions at the integer point of this class of equations.The existence of almost periodic solutions and the uniqueness of this kind of solutions on this class of equations are investigated by using of eigenvalue of corresponding homogeneous difference equations,almost periodic sequence solutions of relevant difference equations and some properties of almost periodic functions and almost periodic sequences.

关 键 词：概周期解 概周期序列解 微分方程 差分方程 逐段常变量 

分 类 号：O177[理学—数学]