Abstract
We are mainly concerned with existence, non-existence and the behavior at infinity of non-negative blow-up entire solutions of the equation Δ u = ρ ( 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.
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