  This paper is principally devoted to revisit the remarkable works of Keller
and Osserman and generalize some previous results related to the those for the
class of quasilinear elliptic problem $$
  \left\{ \begin{array}{l}
  {\rm{div}} \left( \phi(|\nabla u|)\nabla u\right) = a(x)f(u)\quad \mbox{in }
\Omega,\\ u\geq0\ \ \mbox{in}\ \Omega,\ \ u=\infty\ \mbox{on}\ \partial\Omega,
\end{array} \right. $$ where either $\Omega \subset \mathbb{R}^N$ with $N \geq
1$ is a smooth bounded domain or $\Omega = \mathbb{R}^N$. The function $\phi$
includes special cases appearing in mathematical models in nonlinear
elasticity, plasticity, generalized Newtonian fluids, and in quantum physics.
The proofs are based on comparison principle, variational methods and
topological arguments on the Orlicz-Sobolev spaces.
