A variational semilinear singular system

In this paper we study existence of solutions for the following variational semilinear singular system: {u>0inΩ,u∈H01(Ω):−div(A(x)∇u)=θzpu1−θ,z>0inΩ,z∈H01(Ω):−div(M(x)∇z)=puθzp−1, where ΩΩ is a bounded open subset of RN,N>2,ARN,N>2,A and MM are bounded measurable elliptic matrices, and pp and θθ are such that 0<θ<1,p>0,θ+p<2∗.