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 {align*} {cases} -Δ u=(∫Ω_ε{u^{2μ^*}}{|x-y|μ}dy)u^{2μ^*-1}, & in Ω_ε, \\ u=0, & on ∂Ω_ε, {cases} {align*} where 2μ^*=2N-μ/N-2 is the upper critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality, N≥ 5, 0<μ<4 with μ sufficiently close to $0$, Ω_ε:=Ω B(0,ε) and Ω is a bounded smooth domain in RN, which contains the origin, and ε is a positive parameter. As ε goes to zero, we construct bubble solution which blows up at the origin.