一类偏微分方程特征值的上界估计

Upper bound of eigenvalues for a partial differential equations

考虑一类偏微分方程特征值的上界估计,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,其估计系数与区域的度量无关,这个结果在力学和物理学中有着广泛的应用。

The estimates of upper bound for eigenvalues of a partial differential equation are considered.The methods of subsection integration,Rayleigh theorem and inequality estimate were used to obtain upper bound of the inequality which use the preceding n eigenvalues to estimate the（n＋1）th eigenvalue,meanwhile the factor is independence to the measure of the domain.The result have wide application in mechanics and physics.