正则微分算子带权第二特征值的上界

Estimate of the Upper Bound of Second Eigenvalue with Weight for Canonical Differential Operator

考虑某类正则微分算子的带权第二特征值上界估计的问题。利用试验函数、分部积分、Rayleigh定理和不等式等方法与技巧,得到了用正则微分算子的第一个特征值来估计第二个特征值的不等式,其估计系数与区间的几何度量无关。其不等式在物理学和力学中应用广泛,在微分方程的理论研究中起着重要的作用。

This paper considers the estimate of the upper bound of second eigenvalue with weight for canonical differential operator. The upper of second eigenvalue is dependent on the first eigenvalue by using integral, Rayleigh theorem and inequality estimation. The estimate 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.