微分算子带一般权第二特征值的上界估计

Upper Bound Estimate of Second Eigenvalue of Differential Operator with General Weight

研究考虑微分算子带一般权第二特征值的上界估计的问题。充分利用试验函数、多次分部积分、Rayleigh定理、Wirtinger不等式和Schwarz不等式等方法与技巧,计算得到了用微分算子带一般权的第一个特征值来估计第二个特征值的上界估计的不等式,其估计系数是比较好的、恰当的,并且是全新的。微分算子带一般权第二特征值的上界估计在物理学和力学中应用非常广泛,并且在微分方程的理论研究中起着重要的作用。

This paper considers the upper bound estimate of the second eigenvalue of the differential operator with general weight. Based on testing function,multiple partial integration,Rayleigh theorem,Wirtinger inequality and Schwarz inequality,this paper obtains the inequality of upper bound estimate by using first eigenvalue of the differential operator with general weight to estimate second eigenvalue. The estimate coefficients are better,more appropriate and completely new. The upper bound estimate of the second eigenvalue of the differential operator with general weight is widely used in physics and mechanics,and it plays a significant role in the theoretical research of differential equations.