Existence of global solutions of elliptic systems

We study existence of entire solutions of elliptic systems whose prototype is given by div |u|γ |∇u|m−2∇u − γ m|u|γ−2u|∇u|m = |u|p−2u, u:Rn →RN, withm>1, γ ∈ R, p >1. In particular, we prove that, if γ p −m, the system above admits a one parameter family of nontrivial entire radial solutions, u = u(|x|), such that lim|x|→∞ |u(|x|)| =∞.  2004 Elsevier Inc. All rights reserved