时标上带扰动动态方程周期解的存在性

Existence of periodic solutions of perturbed dynamic equations on time scales

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.