四阶微分系统第二特征值的上界估计

Estimate of the Upper Bound of Second Eigenvalue for the Differential System with Four Orders

研究四阶微分系统第二特征值的上界估计.利用试验函数、Rayleigh定理、分部积分和Schwartz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,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 estimate of the upper bound of second eigenvalue for the differential system with four orders. The upper of second eigenvalue is dependent on the first eigenvalue by using integral, Rayleigh theorem and inequality estimation. The estimate coefficients do not depend on the measure of the domain in which the problem is concerned. This kind of problem is significant both in the theory of differential equations and in the application to mechanics and physics.