Bound states of fractional Choquard equations with Hardy-Littlewood-Sobolev critical exponent

We deal with the fractional Choquard equation where I-mu(x) is the Riesz potential, s is an element of (0, 1), 2s< N not equal 4s, 0 < mu < min{N, 4s} and 2* mu,s= 2N- mu/N-2s is the fractional critical Hardy-Littlewood-Sobolev exponent. By combining variational methods and the Brouwer degree theory, we investigate the existence and multiplicity of positive bound solutions to this equation when V(x) is a positive potential bounded from below. The results obtained in this paper extend and improve some recent works in the case where the coefficient V(x) vanishes at infinity.