四阶线性微分方程组的离散谱估计

Estimates for Discrete Spectrum of System of Linear Differential Equations with Four Orders

考虑四阶线性微分方程组的离散谱估计 ,利用矩阵运算、分部积分和不等式估计等方法与技巧 ,得到了用前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 。

This paper describes the estimates for discrete spectrum of system of linear differential equations with four orders. The upper bounds of the (n+1) th eigenvalue are shown by the first n eigenvalues by using matrix, integral and inequality estimation. The estimate coefficients do not depend on the domain in which the problem is concerned. The results are widely used in physics and mechanics.