高阶微分系统特征值的上界估计(英文)

Estimate of Eigenvalues' Upper Bound for High-Order Differential System

考虑高阶微分系统特征值的上界估计。利用正定矩阵、分部积分、Rayleigh定理和不等式估计等方法,首先将问题化为矩阵形式,建立了Rayleigh不等式,其次证明了三个引理,最后获得了用前n个特征值来估计第n+1个特征值的上界的不等式,其估计系数与区间的几何度量无关,其结果是文献[1-4]的进一步拓展。

With the consideration of estimate of the eigenvalues＇ upper bound for high-order differential system, we change the system into matrix form, and then use positive definite matrix, integration by parts and Rayleigh theorem to obtain a basic inequality. Secondly, for clearness, we divide the proof into three lemmas. At last, the main results turn out immediately. These estimates are that the （ n ＋ 1 ） th eigenvalue is bounded from above by an amount depending on the former n eigenvalues and being independent on the measure of the domain in which the problem is concerned. Theorems inferred from this paper have expanded the results in the bibliozraphv.