关于Borg定理  

On Borg's theorem

作　　者：谢惠琴[1] 史金麟[1] 

机构地区：[1]福州大学数学与计算机科学学院,福建福州350002

出　　处：《纯粹数学与应用数学》2008年第3期438-443,共6页Pure and Applied Mathematics

基　　金：国家自然科学基金数学天元基金(10726062);福州大学科技发展基金(0030824775)

摘　　要：Borg定理是判定周期系数二阶线性微分方程稳定的一个重要定理,这个定理在一定意义下是不可改进的.本文利用判别式的一个新形式,在弱的限制下,得到判定周期系数二阶线性微分方程稳定的定理,所得结论改进了Borg定理的判定结果.Borg＇s Theorem is an important theorem which determine the stability of second order linear differential equation with periodic coefficient, and it is impossible to improve this Theorem in some significance. In this paper, by a new form of discriminant, we obtain theorems which determine the stability of second order linear differential equation with periodic coefficient and improve the result of determination on Borg＇s Theorem under weak constrain.

关 键 词：周期系数 二阶线性微分方程 稳定性 

分 类 号：O175.1[理学—数学]