Existence of positive radial solutions for some nonvariational superlinear elliptic systems

The system under consideration is−Δu+cu=g(u,v)+up,u=u(x),x∈B⊂RN,u|∂B=0,−Δv+dv=h(u,v)+vq,v=v(x),v|∂B=0, where c,d⩾0c,d⩾0 are constants, B   is a ball and 10u,v>0 in B.