Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (3): 830-840.doi: 10.1016/S0252-9602(10)60082-3

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INFINITELY MANY SOLUTIONS FOR A SINGULAR ELLIPTIC EQUATION INVOLVING CRITICAL SOBOLEV-HARDY EXPONENTS IN RN

HE Xiao-Ming, ZOU Wen-Ming   

  1. School of |Sciences, Central University for Nationalities, Beijing 100081, China; Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
  • Received:2007-10-09 Online:2010-05-20 Published:2010-05-20
  • Supported by:

    Supported by NSFC (10971238, 10871109)

Abstract:

In this article, we study the existence of multiple solutions for the singular semilinear elliptic equation involving critical Sobolev-Hardy exponents 
 -?u-u u/|x|2=α |u|2*(s)-2u/|x|βa(x)|u|r-2 u,   x ∈ RN.
By means of the concentration-compactness principle and minimax  methods, we obtain infinitely many solutions which tend to zero for suitable positive parameters α, β.

Key words: Singular elliptic equation, Multiple solutions, Critical Sobolev-Hardy exponent, Minimax method

CLC Number: 

  • 35J60
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