Existence of positive radial solutions for a semilinear elliptic system without variational structure

In this article we consider (component-wise) positive radial solutions of a weakly coupled semilinear elliptic system in a ball with homogeneous Dirichlet data. We deal with a nonvariational problem. We show that the existence results recently obtained by Zou, while very general, nevertheless do not include all cases where existence can be proved.