  We analyze the semilinear elliptic equation $\Delta u=\rho(x) f(u)$, $u>0$ in
${\mathbf R}^D$ $(D\ge3)$, with a particular emphasis put on the qualitative
study of entire large solutions, that is, solutions $u$ such that
$\lim_{|x|\rightarrow +\infty}u(x)=+\infty$. Assuming that $f$ satisfies the
Keller-Osserman growth assumption and that $\rho$ 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.
