一类偏微分方程特征值的估计

摘要

考虑一类偏微分方程特征值的估计，利用Rayleigh定理、分部积分法和不等式估计等方法，得到第k+1个特征值用前k个特征值来估计的不等式，这个结果有广泛的应用价值。%This paper addresses the estimates of eigenvalues of a partial differential equation.We construct some test function and then use Rayleigh theorem to basic inequality.These estimates are that the (k+1)th eigenvalue is bounded from above by an amount depending on thefirstk eigenvalues and independent of the measure of the domain in which the problem is concerned.This kind of problem is significant in potential application to mechanics and physics.