Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (3): 939-948.doi: 10.1016/S0252-9602(10)60091-4

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UNIVERSAL BOUNDS FOR EIGENVALUES OF LAPLACIAN OPERATOR WITH ANY ORDER

 HUANG Guang-Yue, CHEN Wen-Yi   

  1. College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China|School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2007-12-18 Revised:2008-02-29 Online:2010-05-20 Published:2010-05-20
  • Supported by:

    This research is supported by NSFC (10471108, 10631020) of China and NSF of Henan Provincial Education Department (2010A110008)

Abstract:

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 uu    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

CLC Number: 

  • 35P15
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