  We consider local weak large solutions with its blow-up rate near the
boundary to certain class of degenerate and/or singular quasilinear elliptic
equation\\ ${\rm div}(d^{\alpha}(x,\partial{}B)\Phi_p(\nabla u)) = b(x)f(u)$ in
a ball B, where $f$ is normalized regularly varying at infinity with index
$\sigma+1>p-1,\ p>1$. In particular, how the asymptotic behavior of the
solution changes over the varying index and degeneracy and/ or singularity
present in the equation. We also include the second order blow-up rate for the
corresponding semilinear problem.
