ESTIMATES FOR |EIGENVALUES |OF FOURTH-ORDER WEIGHTED POLYNOMIAL OPERATOR

doi:10.1016/S0252-9602(11)60279-8

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (3): 826-834.doi: 10.1016/S0252-9602(11)60279-8

ESTIMATES FOR |EIGENVALUES |OF FOURTH-ORDER WEIGHTED POLYNOMIAL OPERATOR

孙和军, 陈大广

Department of Applied Mathematics, College of Science, Nanjing University of Science and Technology, Nanjing 210094, China|Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

收稿日期:2009-07-15 修回日期:2009-12-12 出版日期:2011-05-20 发布日期:2011-05-20
基金资助:
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).

ESTIMATES FOR |EIGENVALUES |OF FOURTH-ORDER WEIGHTED POLYNOMIAL OPERATOR

SUN He-Jun, CHEN Da-Guang

Department of Applied Mathematics, College of Science, Nanjing University of Science and Technology, Nanjing 210094, China|Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received:2009-07-15 Revised:2009-12-12 Online:2011-05-20 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).

摘要/Abstract

摘要：

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 Λ_k+1in terms of the first k eigenvalues. Moreover, these results contain some results for the biharmonic operator.

关键词: eigenvalue, polynomial operator, biharmonic operator

Abstract:

In this paper, we investigate the Dirichlet eigenvalue problem of fourth-order weighted polynomial operator

Key words: eigenvalue, polynomial operator, biharmonic operator

中图分类号:

35P15

孙和军, 陈大广. ESTIMATES FOR |EIGENVALUES |OF FOURTH-ORDER WEIGHTED POLYNOMIAL OPERATOR[J]. 数学物理学报(英文版), 2011, 31(3): 826-834.

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.

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ESTIMATES FOR |EIGENVALUES |OF FOURTH-ORDER WEIGHTED POLYNOMIAL OPERATOR

ESTIMATES FOR |EIGENVALUES |OF FOURTH-ORDER WEIGHTED POLYNOMIAL OPERATOR

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