Coercive elliptic systems with gradient terms

In this paper we give a classification of positive radial solutions of the following system Δu=v^m, Δv=h(|x|)g(u)f(|∇u|), in the open ball B_R, with m>0, and f, g, h nonnegative nondecreasing continuous functions. In particular, we deal with both explosive and bounded solutions. Our results involve a generalization of the well-known Keller–Osserman condition. Moreover, in the second part of the paper, the p-Laplacian version of the above system is treated. When p≥2, we prove a necessary condition for the existence of a solution with at least a blow up component at the boundary.