摘要
应用平均法研究了时标上带有扰动的动态方程的周期解的存在性,同时将时标上带有扰动的动态方程的平均法进一步推广到ε的二阶情形.受连续系统经典结果的启发,由于时标既包含连续的时间又包含离散的时间,因而时标上的微积分、复合函数求导法则和指数函数等都有新的定义,所以时标情况的平均定理证明起来会更加复杂,应用也更为广泛.
By means of average method,it was studied the existence of periodic solutions of dynamic equations with perturbations on time scales.At the same time,the average method of dynamic equation with disturbance on time scale was further extended to the second order.The proof of this paper was inspired by the classical results of continuous systems,because the time scale included both continuous time and discrete time,there were new definitions for calculus,derivation rule of composite function and exponential function on the time scale,so the proof of average theorem in the case of time scale were more complex and widely.
作者
郭瑞超
GUO Rui-chao(College of Applied Mathematics,Jilin University of Finance and Economics,Changchun 130117,China)
出处
《吉林师范大学学报(自然科学版)》
2021年第4期62-65,共4页
Journal of Jilin Normal University:Natural Science Edition
基金
国家自然科学基金项目(12001224)
吉林省教育厅科学技术项目(JJKH20200137KJ)。
关键词
周期解
平均方法
时标
扰动的动态方程
periodic solutions
averaging method
time scales
perturbed dynamic equations