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We consider the elliptic equation -Δ⁢u=uq⁢|∇⁡u|p{-\Delta u=u^{q}|\nabla u|^{p}}in ℝn{\mathbb{R}^{n}}for any p>2{p>2}and q>0{q>0}.We prove a Liouville-type theorem, which asserts that any positive bounded solution is constant.The proof technique is based on monotonicity properties for the spherical averages of sub- and super-harmonic functions,combined with a gradient bound obtained by a local Bernstein argument.This solves, in the case of bounded solutions,a problem left open in [2], where the case 0

In this paper we give a classification of positive radial solutions of the following system: