Positive Bound States of Fractional Choquard Equations with Upper Hardy–Littlewood–Sobolev Critical Exponent

Abstract. We are interested in the existence of positive bound solutions for the following fractional Choquard equation: [Formula: see text] where [Formula: see text] is an unbounded exterior domain, [Formula: see text], [Formula: see text] is bounded, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] is the fractional upper Hardy–Littlewood–Sobolev critical exponent, and [Formula: see text] is a nonnegative function. By combining variational methods and the Brouwer degree theory, we investigate the existence of positive bound solutions to this equation when [Formula: see text] and the hole [Formula: see text] are suitably small in some sense. The results obtained in this paper extend and improve on some recent works. Our result also holds true in the case [Formula: see text]; hence, this paper can be viewed as an extension of recent contributions on the Benci–Cerami problem for the fractional Choquard equation.