Bubble solutions for the critical Choquard equation involving fractional Laplacian operator in a pierced domain

This paper is devoted to investigating the following fractional Choquard problem: [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text] is a small parameter. Here, [Formula: see text] with [Formula: see text] being a smooth bounded domain in [Formula: see text] with [Formula: see text], and [Formula: see text] denotes the upper critical exponent in the sense of the Hardy–Littlewood–Sobolev inequality. We construct a family of solutions to the above problem exhibiting volcano-like blow-up behavior as [Formula: see text] goes to zero. This result extends the study of critical Choquard equations to fractional settings with shrinking holes, highlighting the interplay between nonlocality and domain topology.