Acta mathematica scientia, Series B >
ESTIMATES FOR |EIGENVALUES |OF FOURTH-ORDER WEIGHTED POLYNOMIAL OPERATOR
Received date: 2009-07-15
Revised date: 2009-12-12
Online published: 2011-05-20
Supported by
The first author was supported by the National Natural Science Foundation of China (11001130) and the NUST Research Funding (2010ZYTS064). The second author was supported by China Postdoctoral Science Foundation (20080430351).
In this paper, we investigate the Dirichlet eigenvalue problem of fourth-order weighted polynomial operator
Δ2 u -a Δu +b u =Λρu, in Ω ( Rn,
u|∂Ω=∂u/∂ν|∂Ω =0,
where the constants a, b ≥0. We obtain some estimates for the upper bounds of the (k+1)-th eigenvalue Λk+1in terms of the first k eigenvalues. Moreover, these results contain some results for the biharmonic operator.
Key words： eigenvalue; polynomial operator; biharmonic operator
SUN He-Jun , CHEN Da-Guang . ESTIMATES FOR |EIGENVALUES |OF FOURTH-ORDER WEIGHTED POLYNOMIAL OPERATOR[J]. Acta mathematica scientia, Series B, 2011 , 31(3) : 826 -834 . DOI: 10.1016/S0252-9602(11)60279-8
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