多项式微分算子带一般权第二特征值的上界估计  

Estimate of the Upper Bound of Second Eigenvalue with General Weight for Polynomial Differential Operator

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》2014年第2期175-179,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：考虑多项式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,得到了用多项式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 polynomial differential opera- tor. The inequality of the estimate of second eigenvalue of polynomial differential operator is obtained from first eigenvalue by using tes- ting function, partial integration, Rayleigh theorem and Schwarz inequality. The estimate coefficients do not depend on the measure of the domain in which the problem is concerned. The inequality is widely used in physics and mechanics, and it plays a significant role in the theoretical research of differential equations.

关 键 词：多项式微分算子 一般权 特征值 特征函数 上界 估计 

分 类 号：O175.1[理学—数学]