Existence of an elliptic system involving Pucci operator

We study the existence of solutions for the nonlinear elliptic system {−Mλ,Λ+(D2u)=f1(x,u)+h1(u,v)in Ω,−Mλ,Λ+(D2v)=f2(x,v)+h2(u,v)in Ω,u>0,v>0in Ω,u=v=0on ∂Ω, where ΩΩ is a bounded domain, f1f1 is superlinear and f2f2 is sublinear at zero and infinity, h1h1 and h2h2 are perturbation terms. We will show that the system has at least two semi-trivial solutions (u,0)(u,0), (0,v)(0,v) and a nontrivial solution (u∗,v∗)(u∗,v∗).