Existence, non-existence and asymptotic behavior of blow-up entire solutions of semilinear elliptic equations ✩

We are mainly concerned with existence, non-existence and the behavior at infinity of non-negative blowup entire solutions of the equation Δu = ρ(x)f (u) in RN. No monotonicity condition is assumed upon f and, in fact, we obtain solutions with a prescribed behavior both at infinity and at the origin. The method used to get existence is based upon lower and upper solutions techniques while for non-existence we explore radial symmetry, estimates on an associated integral equation and the Keller–Osserman condition. © 2005 Elsevier Inc. All rights reserved