Abstract
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.
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