  We study the fractional laplacian problem (-\Delta)^s u &=& u^p -\epsilon u^q
\quad\text{in }\quad \Omega, u &\in& H^s(\Omega)\cap L^{q+1}(\Omega),u &>&0
\quad\text{in }\quad \Omega, u&=&0 \quad\text{in}\quad
\mathbb{R}^N\setminus\Omega, where $s\in(0,1)$, $q>p\geq \frac{N+2s}{N-2s}$ and
$\epsilon>0$ is a parameter. Here $\Omega\subseteq\mathbb{R}^N$ is a bounded
star-shaped domain with smooth boundary and $N> 2 s$. We establish existence of
a variational positive solution $u_{\epsilon}$ and characterize the asymptotic
behaviour of $u_{\epsilon}$ as $\epsilon\to 0$. When $p=\frac{N+2s}{N-2s}$, we
describe how the solution $u_{\epsilon}$ concentrates and blows up at a
interior point of the domain. Furthermore, we prove the local uniqueness of
solution of the above problem when $\Omega$ is a convex symmetric domain of
$\mathbb{R}^N$ with $N>4s$ and $p=\frac{N+2s}{N-2s}$.
