Note on nontrivial solutions for a class of p-Laplacian systems

We prove the existence of nonzero positive solutions of the p-Laplacian system{−Δpui=fi(x,u) in Ω,i∈{1,..,n},ui=0 on ∂Ω, where u=(u1,..,un), Δpui=div(|∇ui|p−2∇ui), p>1, Ω is a bounded domain in Rn with smooth boundary ∂Ω, fi:Ω×R+n→R+ are allowed to be singular at x∈∂Ω and satisfy some sublinear conditions. Our results improved previously known results in the literature.