Monotonicity and nonexistence results to cooperative systems in the half space

In this paper, we prove the monotonicity and nonexistence of positive bounded solutions to an elliptic system in the half space R+n:Δu+f(u,v)=0Δv+g(u,v)=0in R+n,u=v=0on ∂R+n, where fv⩾0, gu⩾0 and both f and g are convex functions.