四阶微分方程广义第二特征值的上界估计  

Estimation of the Upper Bound of Generalized Second Eigenvalue for the Differential Equation with Four Orders

作　　者：胡志坚[1] 钱椿林[1] 

机构地区：[1]苏州市广播电视大学,江苏苏州215004

出　　处：《江南大学学报（自然科学版）》2005年第4期427-430,共4页Joural of Jiangnan University (Natural Science Edition)　

摘　　要：考虑四阶微分方程广义第二特征值的上界估计,利用试验函数、Rayleigh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上界的不等式,其估计系数与区间的度量无关.The paper presents the estimation of the upper bound of generalized second eigenvalue for the differential equation with four orders. The upper of second eigenvalue is dependent on the first eigenvalue based on integral, Rayleigh theorem and inequality estimation. The estimation 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.

关 键 词：四阶微分方程 特征值 特征函数 上界 估计 

分 类 号：O175.1[理学—数学]