Blow up boundary solutions of some semilinear fractional equations in the unit ball

For γ>0, we are interested in blow up solutions u∈C+(B) of the fractional problem in the unit ball B. We distinguish particularly two orders of singularity at the boundary: solutions exploding at the same rate than δα2−1 (δ denotes the Euclidean distance) and those higher singular than δα2−1. As a consequence, it will be shown that the classical Keller–Osserman condition cannot be readopted in the fractional setting.