Solutions with radial symmetry for a semilinear elliptic system with weights

In this paper, we provide sufficient conditions for the boundedness and unboundedness of the entire solutions for a semilinear elliptic system of the following type Δu=p1|x|fu,v,x∈RN , Δv=p2|x|gu,x∈RN,N≥3.Here p1, f, p2 and g are continuous functions satisfying certain properties. Furthermore, we study the case where the system is not of a variational type. Our results are obtained by a straightforward application of the Arzela-Ascoli theorem.