Very large solutions for the fractional Laplacian: Towards a fractional Keller-Osserman condition

We look for solutions of (-Delta)(s)u + f(u) = 0 in a bounded smooth domain Omega, s is an element of (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 derivative 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.