偶数阶微分系统主次特征值之比的下界  

Lower Bound of the Ratio of Principal Eigenvalue to Secondary One for Even-Order Differential System

作　　者：黄振明[1] HUANG Zhen-ming(Department of Mathematics and Physics,Suzhou Vocational University,Suzhou 215104,China)

机构地区：[1]苏州市职业大学数理部,江苏苏州215104

出　　处：《三明学院学报》2018年第2期17-24,共8页Journal of Sanming University

摘　　要：对偶数阶微分系统在齐次边界条件下的主次特征值进行定量分析,借助Sturm-Liouville理论、矩阵和向量运算、分部积分和Rayleigh原理等方法,证明了所选择的试验函数与主特征值、主特征向量间的关系,获得了主次特征值之比的下界估计不等式,此界与系统的系数、阶数有关,而与系统中方程的个数、区间的几何度量无关,且估计结论改进了参考文献中相似估计的精度。Quantitative analysis of principal and secondary eigenvalues for even-order differential system under homogeneous boundary conditions is considered in this paper.The relationship among the selected trial function,the principal eigenvalue and its eigenvector is proved with the help of Sturm-Liouville theory,matrix and vector operation,integration by parts and Rayleigh theorem etc..The estimated inequality of the lower bound of the ratio of principal eigenvalue to secondary one is obtained.This bound is dependent of the system’s coefficients and order,but irrelevant to the number of equations and the geometric measure of the interval.The accuracy of the similar estimate in the bibliography is improved in this paper.

关 键 词：偶数阶微分系统 主次特征值 SCHWARZ不等式 下界估计 

分 类 号：O175.1[理学—数学]