正则高阶微分系统带权第二特征值的上界

Upper Bound of Second Eigenvalue with Weight for the Canonical Differential System with High Orders

考虑正则高阶微分系统带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.

This paper considers the estimation of the upper bound of second eigenvalue for the canonical diftbrential system with high orders. The upper of second eigenvalue is dependent on the first eigenvalue by using integral, rayleigh theorem and inequality estimation.The estimation coefficients do not depend on the measure of the domain its which the problem is concerned. This kind of problem is significant both in theory of differential equations and in application to mechanics and physics.