We analyze the semilinear elliptic equation Δu=ρ(x)f(u), u>0 in
RD(D≥3), with a particular emphasis put on the qualitative
study of entire large solutions, that is, solutions u such that
lim∣x∣→+∞u(x)=+∞. Assuming that f satisfies the
Keller-Osserman growth assumption and that ρ decays at infinity in a
suitable sense, we prove the existence of entire large solutions. We then
discuss the more delicate questions of asymptotic behavior at infinity,
uniqueness and symmetry of solutions.Comment: Journal of Differential Equations 2012, 28 page