  We look for solutions of $(-\Delta)^s u+f(u) = 0$ in a bounded smooth domain
$\Omega$, $s\in(0,1)$, with a strong singularity at the boundary. In
particular, we are interested in solutions which are $L^1(\Omega)$ and higher
order with respect to dist$(x,\partial\Omega)^{s-1}$. We provide sufficient
conditions for the existence of such a solution. Roughly speaking, these
functions are the real fractional counterpart of "large solutions" in the
classical setting.
