Carathéodory方程的平均化（英文）  

Averaging for Carathéodory Equations

作　　者：马学敏[1] 李宝麟[2] 

机构地区：[1]甘肃中医药大学定西校区数学系,甘肃定西743000 [2]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《应用数学》2017年第3期684-692,共9页Mathematica Applicata

基　　金：Supported by The National Natural Science Foundation of China(10771171);555 Innovation Talent Project of Gansu Province(GS-555-CXRC);Technique Innovation Project of Northwest Normal University(NWNU-KJCXGC-212);Important Foundation of Dingxi Teachers College(TD2016ZD06)

摘　　要：本文中,我们通过利用平均化方法,将非自治常微分方程转化成自治方程,刻画了其平均化过程,得到非自治方程的平均化方程,而且利用Henstock-Kurzweil积分,建立了Carathéodory方程的周期和非周期的平均化定理.In the paper, we can transfer the non-autonomous ordinary differential equation into autonomous equation by using the averaging methods, so the process of averaging is described and the averaging equation of non-autonomous equation is obtained.Furthermore, by using Henstock-Kurzweil integral, both periodic and non-periodic averaging theorems for Carath′eodory equations are established.

关 键 词：平均化方法 Henstock-Kurzweil积分 Carathéodory方程 周期平均化 非周期平均化 

分 类 号：O175.14[理学—数学]