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

doi:10.1016/S0252-9602(10)60082-3

Abstract

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|^s+ βa(x)|u|^r-2 u, x ∈ R^N.
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

HE Xiao-Ming, ZOU Wen-Ming. INFINITELY MANY SOLUTIONS FOR A SINGULAR ELLIPTIC EQUATION INVOLVING CRITICAL SOBOLEV-HARDY EXPONENTS IN R^N[J].Acta mathematica scientia,Series B, 2010, 30(3): 830-840.

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INFINITELY MANY SOLUTIONS FOR A SINGULAR ELLIPTIC EQUATION INVOLVING CRITICAL SOBOLEV-HARDY EXPONENTS IN R^N

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