Existence of positive solutions for a semilinear elliptic problem with critical Sobolev and Hardy terms

Let N ≥ 4 N\geq 4 , let 2 ∗ = 2 N / ( N − 2 ) 2^{\ast }=2N/(N-2) and let Ω ⊂ R N \Omega \subset \mathbb {R}^{N} be a bounded domain with a smooth boundary ∂ Ω \partial \Omega . Our purpose in this paper is to consider the existence of solutions of the problem: \[ { − Δ u − μ u | x | 2 a m p ; = | u | 2 ∗ − 1 a m p ; a m p ; in  Ω , u a m p ; > 0 a m p ; a m p ; in  Ω , u a m p ; = 0 a m p ; a m p ; on  ∂ Ω , \left \{ \begin {aligned} -\Delta u - \mu \frac {u}{\vert x\vert ^2} &= \vert u\vert ^{2^\ast -1} && \text {in $\Omega $}, \\ u & > 0 && \text {in $\Omega $},\\ u & = 0 && \text {on $\partial \Omega $}, \end {aligned} \right . \] where 0 > μ > ( N − 2 2 ) 2 . 0>\mu >(\frac {N-2}{2})^{2}.