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.
出处
《纯粹数学与应用数学》
CSCD
北大核心
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)
关键词
周期系数
二阶线性微分方程
稳定性
periodic coefficient, second order linear differential equation, stability
