Existence of a cooperative elliptic system involving pucci operator

The authors study the existence of solutions for the nonlinear elliptic system {-Mλ,Λ+(D2u)=f(u,υ)inΩ,-Mλ,Λ+(D2υ)=g(u,υ)inΩ,u≥0,υ≥0inΩ,u=0,υ=0on∂Ω,where ω is a bounded convex domain in ℝN, N ≥ 2. It is shown that under some assumptions on f and g, the problem has at least one positive solution (u, v).