Entire large solutions for semilinear elliptic equations
Résumé
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. © 2012 Elsevier Inc.