For $\gamma>0$, we are interested in blow up solutions $u\in C^+(B)$ of the fractional problem in the unit ball $B$ \begin{ equation}\label{ 2nov} \left\{ \begin{ array} { rcll} \Delta^{ \frac{ \alpha}{ 2}} u &=& u^\gamma&\ \text{ in }B\\ u &=& 0&\ \text{ in }B^c.\end{ array}\right. \end{ equation} We distinguish particularly two orders of singularity at the boundary: solutions exploding at the same rate than $\delta^{ 1-\frac{ \alpha}{ 2}}$ ($\delta$ denotes the Euclidean distance) and those higher singular than $\delta^{ 1-\frac{ \alpha}{ 2}}.$ As a consequence, it will be shown that the classical Keller-Osserman condition can not be readopted in the fractional setting.
Categories: math.AP