Entire positive solution to the system of quasilinear elliptic equations

The quasilinear elliptic systemdiv(|∇u|p-2∇u)+f1(x)uα1+g1(x)u-β1+h1(x)uγ1Q(v)=0,div(|∇v|q-2∇v)+f2(x)vα2+g2(x)v-β2+h2(x)vγ2Q(u)=0with p,q>1,0<α1,β1,γ1