一类任意阶微分方程第二特征值的上界估计

Estimate of the Upper Bound of Second Eigenvalue for the Differential Equation with any Order

考虑了一类任意阶微分方程第二特征值的上界估计 ,获得了用第一特征值来估计第二特征值的上界不等式 ,其估计系数与区间的度量无关 .此结果在物理学和力学中有着广泛的应用 。

This paper considers the estimate of the upper bound of second eigenvalue for the differential equation with any order.The upper of second eigenvalue is dependent on the first eigenvalue,and being independent on the measure of the domain in which the problem is concerned.This kind of problem is significant both in theory of differential equations and in application to mechanics and physics.