Revisiting an idea of Brézis and Nirenberg

Let n⩾3n⩾3 and Ω   be a C1C1 bounded domain in RnRn with 0∈∂Ω0∈∂Ω. Suppose ∂Ω   is C2C2 at 0 and the mean curvature of ∂Ω at 0 is negative, we prove the existence of positive solutions for the equation:equation(0.1){Δu+λun+2n−2+u2∗(s)−1|x|s=0in Ω,u=0on ∂Ω, where λ>0λ>0, 00and1⩽p