Acta mathematica scientia,Series B ›› 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

 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.

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

CLC Number: 

  • 35J20
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