POSITIVE BOUND STATES OF FRACTIONAL CHOQUARD EQUATIONS WITH UPPER HARDY--LITTLEWOOD--SOBOLEV CRITICAL EXPONENT

By combining variational methods and the Brouwer degree theory, we investigate the existence of positive bound solutions to this equation when V (x) and the hole RN\setminus \Omega  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 \Omega =RN; hence, this paper can be viewed as an extension of recent contributions on the Benci--Cerami problem for the fractional Choquard equation.