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

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

孙和军, 陈大广   

  1. 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   

  1. 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:

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

Δ2 u -a Δu +b uρu,     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.

关键词: eigenvalue, polynomial operator, biharmonic operator

Abstract:

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

Δ2 u -a Δu +b uρu,     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

中图分类号: 

  • 35P15