Bubble solution for the critical Hartree equation in pierced domain

In this article, we establish the existence of solutions to the following critical Hartree equation \begin{align*} \begin{cases} -Δu=\left(\int_{Ω_\varepsilon}\frac{u^{2_μ^}}{|x-y|^μ}dy\right)u^{2_μ^-1}, &$\text{ in }$ Ω_\varepsilon, \ u=0, &$\text{ on }$ \partialΩ_\varepsilon, \end{cases} \end{align*} where $2_{\mu }^{\ast }=\frac{2N-\mu }{N-2}$ is the upper critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality, $N\ge 5$, $0<\mu <4$ with $\mu$ sufficiently close to $0$, ${\mathrm{\Omega }}_{\epsilon }:=\mathrm{\Omega }\mathrm{\backslash }B(0,\epsilon )$ and $\mathrm{\Omega }$ is a bounded smooth domain in ${\mathbb{R}}^N$, which contains the origin, and $\epsilon$ is a positive parameter. As $\epsilon$ goes to zero, we construct bubble solution which blows up at the origin.