  In this paper we study positive solutions to problem involving the fractional
Laplacian $(E)$ $(-\Delta)^{\alpha} u(x)+|u|^{p-1}u(x)=0 in
x\in\Omega\setminus\mathcal{C}$, subject to the conditions $u(x)=0$
$x\in\Omega^c$ and $\lim_{x\in\Omega\setminus\mathcal{C},
x\to\mathcal{C}}u(x)=+\infty$, where $p>1$ and $\Omega$ is an open bounded
$C^2$ domain in $\mathbb{R}^N$, $\mathcal{C}\subset \Omega$ is a compact $C^2$
manifold with $N-1$ multiples dimensions and without boundary, the operator
$(-\Delta)^{\alpha}$ with $\alpha\in(0,1)$ is the fractional Laplacian.
  We consider the existence of positive solutions for problem $(E)$. Moreover,
we further analyze uniqueness, asymptotic behaviour and nonexistence.
