一类微分方程解与其平均方程解之间的关系  

The Relationships between a Class of Differential Equations and it's Averaged Equations

作　　者：牛保青[1] 袁静[1] 

机构地区：[1]安阳师范学院数学科学学院,河南安阳455000

出　　处：《广西民族大学学报（自然科学版）》2008年第2期51-54,共4页Journal of Guangxi Minzu University ：Natural Science Edition

摘　　要：研究了一类微分方程解与其平均方程解之间的关系,当相应的平均方程的解为定常解时,我们所得到的原方程的一阶近似解必为周期解;而当相应平均方程的解为周期解时,原方程的一阶近似解必为调幅振动解,且在满足一定的条件下,还可以是周期解.In this paper, the relationships between a class of differential equations and it＇s averaged equations are studied. When the solutions of the corresponding averaged equation are constants, the approximate solutions of order one of the former equation must be periodic solutions. But when the solutions of corresponding averaged equations are periodic solutions, the approximate solutions of order one of the former equation must be oscillatory solutions with amplitude modulated, and may also be periodic solutions if some terms satisfied.

关 键 词：平均方程 周期解 调幅振动 

分 类 号：O175.1[理学—数学]