Singular solutions of fractional elliptic equations with absorption

The aim of this paper is to study the singular solutions to fractional elliptic equations with absorption $$\{\text{arraycolsep}=1pt\begin{array}{ll}(-\mathrm{\Delta }{)}^{\alpha }u+\mathrm{\mid }u{\mathrm{\mid }}^{p-1}u=0,& \mathrm{i}\mathrm{n}\mathrm{\Omega }\setminus \{0\},\\ u=0,& \mathrm{i}\mathrm{n}{\mathbb{R}}^N\setminus \mathrm{\Omega },\\ {\lim }_{x\to 0}u(x)=+\mathrm{\infty },\end{array}$$ where $p>0$, $\mathrm{\Omega }$ is an open, bounded and smooth domain of ${\mathbb{R}}^N(N\ge 2)$ with $0\in \mathrm{\Omega }$. We analyze the existence, nonexistence, uniqueness and asymptotic behavior of the solutions.