摘要
考虑2s和2t阶阶联立微分方程组在Dirichlet和Neumann边界条件下广义特征值的含权估计,此问题由钱椿林教授提出,是某类六阶微分系统特征值问题的自然延伸,所用方法是Hile和Yeh方法的改进和推广,可用于估计重调和算子等的特征值,笔者引入向量和矩阵符号,运用SturmLiouville关于特征值和特征函数空间的定性理论,利用矩阵运算、分部积分、试验函数和Schwartz不等式等具体方法,获到了用主特征值来估计次特征值的显式上界不等式,且其估计系数与所论区间的度量无关,其结论是文献定理的进一步推广.
In this paper, weighted estimate of generalized eigenvalue for 2s and 2t order simultaneous dif-ferential system under the Neumann boundary condition as well as Dirichlet is considered. This problem isthe nature extension of the eigenvalue problem of differential system with sixth order, proposed indirectlyby prof. Qian. The method used here is the extension with some improvements of Hile and Yeh＇s who suc-cessively estimate the eigenvalues of biharmonic operator in bibliography. With the symbol of vector andmatrix, the inequality of the explicit upper bound of the second eigenvalue is estimated from the principaleigenvalue by using Sturm-Liouville＇s qualitative theory of eigenfunction space, matrix operation, integra-tion by parts, trial function and Schwartz inequality etc. The estimate coefficients do not depend on themeasure of the domain in which the problem is discussed. The results expanded the theorems in the bibli-ography.
出处
《海南师范大学学报（自然科学版）》
CAS
2015年第3期250-254,共5页
Journal of Hainan Normal University（Natural Science）
关键词
联立微分方程组
次特征值
权函数
瑞利商
估计
simultaneous differential system
second eigenvalue
weighted function
Rayleigh quotient
estimate
