n级混合微分系统第二特征值的上界不等式

Inequality of the Upper Bound of Second Eigenvalue for the n-stage Mixed Differential System

考虑n级混合微分系统第二特征值的上界估计。利用试验函数、分部积分和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。其结果在常微分方程的研究和应用中起着重要的作用。

This paper considers the inequality of the upper bound of second eigenvalue for the n-stage mixed differential system.The upper of second eigenvalue is dependent on the first eigenvalue by using integral 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 theory of differential equations and in application to mechanics and physics.