任意阶微分算子带一般权第二特征值的上界估计  

The Upper Bound Estimate of Second Eigenvalue with General Weight for Differential Operator with Any Order

作　　者：卢亦平[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12期1490-1494,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：考虑某类任意阶微分算子带一般权第二特征值的上界估计的问题。利用试验函数、分部积分、Rayleigh定理和Schwarz不等式等方法与技巧,得到了用任意阶微分算子的第一个特征值来估计第二个特征值的不等式,其估计系数与区间的几何度量无关。其不等式在物理学和力学中应用广泛,在微分方程的理论研究中起着重要的作用。This paper considers the upper bound estimate of second eigenvalue with general weight for the differential operator with any order. The inequality of upper of second eigenvalue is deduced from first eigenvalue by using testing function, Rayleigh theorem, partial integration and Schwarz inequality. The estimate coefficients do not depend on the measure of the domain in which the problem is concerned. The result is widely used in physics and mechanics, and it plays a significant role in the research of differential equations.

关 键 词：微分算子 一般权 特征值 特征函数 上界 估计 

分 类 号：O175.1[理学—数学]