We obtain necessary conditions expressed in terms of Wiener type tests involving Hausdorff or Bessel capacities for the existence of large solutions to equations (1) $-\Gd_pu+e^{u}-1=0$ or (2) $-\Gd_pu+u^q=0$ in a bouded domain $\Gw$ when $q>p-1>0$. We apply our results to equations (3) $-\Gd_pu+\abs{\nabla u}^{q}+bu^{p-1}=0$, (4) $-\Gd u+\abs{\nabla u}^{2}+u^{q}=0$ and $-\Gd u+u^{-q}=0$ with $q>0$