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By the Karamata regular variation theory and comparison principle, we establish the boundary behavior of positive weak solutions for the problem $$\Delta_{p}u=b(x)f(u), \quad x\in\Omega, \qquad u|_{\partial\Omega}= \infty, $$ where Ω is a bounded domain with smooth boundary in $R^{N}$, the weight $b(x)\in C^{\alpha}(\overline{\Omega})$, which may be vanishing on the boundary and rapidly varying near the boundary, and the nonlinearity f may be rapidly varying at infinity. For the case $f(s)=s^{m}\pm f_{1}(s)$ with sufficiently large s, where $m>p-1$ and $f_{1}$ is normalized regularly varying at infinity with index $m_{1}\in(0,p-1)$, we show the influence of the geometry of Ω on the boundary behavior of solutions. Finally, we prove the existence and uniqueness of the solution for the problem.

The first and second expansion of large solutions for quasilinear elliptic equations with weight functions