An existence of positive solutions to singular elliptic equations

In this paper we study the existence of solutions to the following semilinear elliptic problem {-div(M(x)∇μ) - μu/|x|² = f(x)/u^θ in Ω, u>0 in Ω, u = 0 on ∂Ω, where Ω is an open bounded subset of ℝ^N, N ≥ 3, 0 ε Ω and θ > 0, 0 ≤ f ε L^m(Ω),1< m < N/2, 0<μ < (N-2/2)² The special feature of this problem is that it has singularity at the origin as well as on the boundary of Ω. © 2014 Unione Matematica Italiana.