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

摘要

We are mainly concerned with existence, non-existence and the behavior at infinity of non-negative blow-up entire solutions of the equation Delta u = p(x)f(u) in R-N. 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. (c) 2005 Elsevier Inc. All rights reserved.