正则任意阶微分系统带一般权第二特征值的上界

Estimate of the Upper Bound of Second Eigenvalue with General Weight for the Canonical Differential System with Any Orders

考虑正则任意阶微分系统带一般权第二特征值的上界估计。利用试验函数,Rayleigh定理,分部积分和Schwarz不等式等估计方法与技巧,获得了用第一特征值来估计第二特征值的上界的不等式,其估计系数与区间的度量无关。其结果在物理学和力学中有着广泛的应用,在常微分方程的研究中起着重要的作用。

Considering the estimate of the upper bound of weighted second eigenvalue for differential system with canonical arbitrary or- dera, this paper obtains the inequality for the estimate of the upper bound of second eigenvalue by the first eigenvalue with the estima- tion methods of test function, Rayleigh theorem, integration by part and Schwarz inequality. The estimate coefficients do not depend on the measure of the domain. The result is widely used in physics and mechanics, which plays a significant role in the research of ordina- ry differential equation.