探研六阶微分系统主次特征值之比的下界

On the Lower Bound of the Ratio of Principal Eigenvalue to Secondary One for Differential System with Sixth-order

对六阶微分系统广义低阶特征值进行定量分析,运用经典的Sturm-Liouville特征值定性理论,利用矩阵运算、分部积分、测试函数和Schwartz不等式等具体方法,找到了所论问题的主特征值与主特征向量间的关系,并获得了主次特征值之比的下界估计不等式,此界仅与系统的系数有关,而与所论区间的几何度量无关,其结果是参考文献结论的进一步推广。

The quantitative analysis of generalized lower-order eigenvalues for differential system with sixth-order isconducted in this paper. The relationship between principal eigenvalue and its eigenvector is found by using classicalSturm-Liouville＇s eigenvalue qualitative theory, matrix operation, integration by parts, trial function and Schwartz inequalityetc. The inequality of the lower bound of the ratio of principal eigenvalue to secondary one is also gained. This bound is onlydependent of the system＇s coefficients, but not the measure of the domain in which the problem is concerned. The results arethe further extension of the conclusion of the bibliography.