一类常微分方程特征值的带权估计

Weightd Estimates for Eigenvalues for a Differential Equation

考虑一类常微分方程的特征值的带权估计,利用分部积分、Rayleigh定理和不等式估计等方法,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,其结果在物理学和力学等领域中应用广泛。

This paper considers the estimates for eigenvalues of a differential equation . We construct some test function and then use the Rayleigh theorem to obtain a basic inequality. These estimates are that the （ n ＋ 1 ）th eigenvalues is bounded from above by an amount depending on the first n eigenvalues and being independent of the measure of the domain in which the problem is concerned. This kind of problem is significant is potential application to mechanics and physics.