Solutions for semilinear elliptic equations with critical exponents and Hardy potential

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