微分方程带一般权的第二特征值的上界估计  

The upper bound estimation of second eigenvalue with general weight for differential equations

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》2009年第10期7-9,20,共4页Journal of Changchun University

基　　金：苏州市职业大学基金资助项目(SZD07W61)

摘　　要：考虑微分方程带一般权的第二特征值的上界估计。利用试验函数,Rayle igh定理,分部积分,Schwartz不等式和Young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,在微分方程的研究中起着重要的作用。This paper considers the upper bound estimation of second eigenvalue with general weight for differential equations. The inequality of upper of second eigenvalue is deduced from first eigenvalue by using testing function, Rayleigh theorem, partial integration, Schwartz inequality and Young 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：微分方程 一般权 特征值 特征函数 上界 估计 

分 类 号：O175.1[理学—数学]