数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (6): 2017-2032.doi: 10.1016/S0252-9602(10)60188-9

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INFINITELY MANY SOLUTIONS FOR AN ELLIPTIC PROBLEM INVOLVING CRITICAL NONLINEARITY

曹道民, 严树森   

  1. Institute of Applied Mathematics, AMSS, Chinese Academy of Sciences, Beijing 100190, China Department of Mathematics, The University of New England, Armidale NSW 2351, Australia
  • 收稿日期:2010-08-24 出版日期:2010-11-20 发布日期:2010-11-20
  • 基金资助:

    D.Cao was supported by Key Project (10631030) of NSFC and Knowledge Innovation Funds of CAS in China. S.Yan was partially supported by ARC in Australia.

INFINITELY MANY SOLUTIONS FOR AN ELLIPTIC PROBLEM INVOLVING CRITICAL NONLINEARITY

 CAO Dao-Min, YAN Shu-Sen   

  1. Institute of Applied Mathematics, AMSS, Chinese Academy of Sciences, Beijing 100190, China Department of Mathematics, The University of New England, Armidale NSW 2351, Australia
  • Received:2010-08-24 Online:2010-11-20 Published:2010-11-20
  • Supported by:

    D.Cao was supported by Key Project (10631030) of NSFC and Knowledge Innovation Funds of CAS in China. S.Yan was partially supported by ARC in Australia.

摘要:

We study the following elliptic problem:
{−div(a(x)Du) = Q(x)|u|2*-2uu      x ∈Ω,
  u = 0                                                 on∂Ω.
Under certain assumptions on a and Q, we obtain existence of infinitely many solutions by variational method.

关键词: semilinear elliptic equations, infinitely many solutions, variational method

Abstract:

We study the following elliptic problem:
{−div(a(x)Du) = Q(x)|u|2*-2uu      x ∈Ω,
  u = 0                                                 on∂Ω.
Under certain assumptions on a and Q, we obtain existence of infinitely many solutions by variational method.

Key words: semilinear elliptic equations, infinitely many solutions, variational method

中图分类号: 

  • 35J20