Acta mathematica scientia, Series B >
UNIVERSAL BOUNDS FOR EIGENVALUES OF LAPLACIAN OPERATOR WITH ANY ORDER
Received date: 2007-12-18
Revised date: 2008-02-29
Online published: 2010-05-20
Supported by
This research is supported by NSFC (10471108, 10631020) of China and NSF of Henan Provincial Education Department (2010A110008)
Let Ω be a connected bounded domain in Rn. Denote by λi the i-th eigenvalue of the Laplacian operator with any order p:
{(-?)p u=λu in Ω,
u=∂u /∂n =…=∂p-1u / ∂n p-1=0 on ∂Ω.
In this article, we give some expressions for upper bound of the (k+1)-th eigenvalue λk+1 in terms of the first k eigenvalues.
Key words： Eigenvalue; Laplacian operator
HUANG Guang-Yue , CHEN Wen-Yi . UNIVERSAL BOUNDS FOR EIGENVALUES OF LAPLACIAN OPERATOR WITH ANY ORDER[J]. Acta mathematica scientia, Series B, 2010 , 30(3) : 939 -948 . DOI: 10.1016/S0252-9602(10)60091-4
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