On the existence of positive solution for a class of singular systems involving quasilinear operators

In this paper we consider the existence of positive solution for the following class of singular systems-Δpu=1vγ1+vα1,-Δqv=1uγ2+uα2inΩ,u,v>0inΩ,u=v=0on∂Ω,where Ω⊂RN,N⩾2, is a smooth bounded domain, Δp and Δq are, respectively, the p-Laplacian and q-Laplacian, with p, q > 1, and α1, α2, γ1 and γ2 are positive constants. The main tools used are a result due to Rabinowitz and a Hardy-Sobolev inequality.