On the radial solutions of a system with weights under the Keller–Osserman condition

We establish conditions on the functions p1p1 and p2p2 that are necessary and sufficient for the existence of positive solutions, bounded and unbounded, of the semilinear elliptic system{Δu=p1(|x|)f1(u,v) for x∈RN(N⩾3),Δv=p2(|x|)f2(u,v) for x∈RN(N⩾3), where p1p1, p2p2, f1f1 and f2f2 are continuous functions satisfying certain properties.