任意阶微分系统带权第二特征值的上界  

Upper Bound of Weighted Second Eigenvalue for Differential Systems with Arbitrary Orders

作　　者：赵晓苏[1] 钱椿林[1] 

机构地区：[1]苏州市职业大学基础部,江苏苏州215104

出　　处：《长春大学学报》2012年第8期975-979,共5页Journal of Changchun University

基　　金：苏州市职业大学基金资助项目(2010SZDQ12)

摘　　要：考虑任意阶微分系统带权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,其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。Considering the estimate of the upper bound of weighted second eigenvalue for differential systems with arbitrary orders, this paper, using test functions, Rayleigh Theorem, integration by part, Schwartz inequality estimation, obtains the inequality for the estimate of upper bound of the second eigenvalue by the first eigenvalue and the estimation coefficients do not depend on the measure of the domain. The result is widely used in physics and mechanics, which plays an important role in the study of ordinary differential equation.

关 键 词：任意阶微分系统 特征值 特征向量 上界 

分 类 号：O175.1[理学—数学]