Existence and Nonexistence of Entire Large Solutions for Some Semilinear Elliptic Equations

Abstract

In this note, we consider positive entire large solutions for semilinear elliptic equations Δu = ρ(x)f(u) in R^N with N ≥ 3. More precisely, we are interested in the link between the existence of entire large solution with the behavior of solution for -Δu = ρ(x) in R^N. Especially for the radial case, we try to give a survey of all possible situations under Keller-Osserman type conditions.