In this paper, we study the existence of entire solutions for the following elliptic system                                          △mu = p(x) f(v), △l v = q(x) g(u),   x ∈ RN, where 1 < m, l < ∞, f, g are continuous and non-decreasing on [0,∞), satisfy f(t) > 0, g(t) > 0 for all t > 0 and the Keller-Osserman condition. We establish conditions on p and q that are necessary for the existence of positive solutions, bounded and unbounded, of the given equation.