Infinitely many solutions for a singular elliptic equation involving critical Sobolev-Hardy exponents in R N

Abstract

In this article, we study the existence of multiple solutions for the singular semilinear elliptic equation involving critical Sobolev-Hardy exponents - Δ u - μ u | x | 2 = α | u | 2 * ( s ) - 2 u | x | s + β α ( 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.