多项式Laplace算子的特征值估计

An Estimate for Eigenvalues of Polynomial Laplacian Operator

讨论了多项式Laplace算子Dirichlet问题,首先通过选取适当的函数,根据RayLeigh-Ritz不等式,得到了该问题用前k个特征值来估计第k+1个特征值的不等式,然后通过选取适当的系数,发现不等式蕴含成庆明和杨洪苍的结论及吴发恩和曹林芬的结论,且根据Chebyshev不等式等,证明了该不等式优于陈祖墀和钱春林的结论.

The paper chiscusses the eigenvalues of polynomial Laplacian operator Dirchlet problem, First, by choosing appropriate function and according to RayLeigh-Ritz inequality, we get an inequality estimate for apper bound of k ＋ 1 in terhns of the first k eigenualues. Then, by choosing appropriate cofficient, we finds the inequatity contains the conclusion of Wu an Cao＇s and Cheng and Yang＇s. Finally, auording to the Cheby sheu inequality etc, we proofs that the inequality is better than that of chen and Qian＇s.