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.