Bubble solution for the critical Hartree equation in a pierced domain

In this article, we establish the existence of solutions to the following critical Hartree equation:$\begin{align*} \begin{cases} -\Delta u = \left(\int_{\Omega_\varepsilon}\frac{u^{2_{\mu}^*}}{|x-y|^{\mu}}dy\right)u^{2_{\mu}^*-1}, &\text{ in } \Omega_\varepsilon, \\ u = 0, &\text{ on } \partial\Omega_\varepsilon, \end{cases} \end{align*}$where $ 2_{\mu}^* = \frac{2N-\mu}{N-2} $ is the upper critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality, $ N\geq 3 $, $ 0<\mu<4 $, $ \Omega_\varepsilon: = \Omega\backslash B(0,\varepsilon) $ where $ \Omega $ is a bounded smooth domain in $ \mathbb{R}^N $ which contains the origin, and $ \varepsilon $ is a positive parameter. As $ \varepsilon $ goes to zero, we construct a bubble solution which blows up at the origin.