In this paper, we answer affirmatively an open problem (cf. Theorem 4′ in Ferrero and Gazzola (J. Differential Equations 177 (2001) 494): Let Ω∋0 be an open-bounded domain, Ω⊂R N(N⩾5) and assume that 0⩽μ<( N−2 2 ) 2−( N+2 N ) 2 , then, for all λ>0 there exists a nontrivial solution with critical level in the range (0, 1 N S μ N 2 ) for the problem −Δu−μ u |x| 2 =λu+|u| 2 ∗−2 u in Ω; u=0 on ∂Ω.