Existence of Concentrating Solutions for Critical Hartree Equations in Perforated Domains

In this paper, we study a critical Hartree equation with mixed boundary conditions in a perforated domain. By means of the Lyapunov–Schmidt reduction method, we prove that when the radius ε of the hole is sufficiently small, the problem admits, for each sufficiently small ε>0, a positive solution uε concentrating and blowing up near the center of the hole. Moreover, we characterize its concentration point, scaling parameter and main asymptotic profile.