高阶微分方程的特征值估计

运用试验函数和Rayleigh定理得到了一个基本不等式，证明了三个引理。建立了用前n个特征值来估计第n 1个特征值的上界的不等式，其估计系数与区间的几何度量无关，其结果在物理学和力学中应用广泛。

Estimates for Eigenvalues of Differential Equation with Higher Orders

This paper studies and estimates for eigenvalues of differential equation with higher orders.First of all,we construct some test function and then use the Rayleigh theorem to obtain a basic inequality;secondly,we divide the proof into three lemmas;at last,the main results are obtained.These estimates are that the (n 1)th eigenvalues is bounded from above by an amount depending on the first n eigenvalues and that it is independent of the measure of the domain.This kind of problem is significant for its potential application in mechanics and physics.