On a class of singular elliptic systems

We study the semilinear elliptic system {−Δu=u−p+v−q,u>0inΩ,−Δv=u−r+v−s,v>0inΩ,u=v=0on  ∂Ω, where Ω⊂RN(N≥1) is a smooth and bounded domain, p,q,r,s>0p,q,r,s>0. Under suitable ranges of exponents we obtain various results regarding the well posedness of our system.