In this paper, we study the following Choquard equations with fractional Laplacian ⎧ ⎨ ⎩ (-⠂)su + u = (I & alpha; * |u|p)|u|p-2u in RN, lim |x|& RARR;& INFIN; u(x)=0, u & ISIN;Hs(RN), where (-⠂)s is the fractional Laplacian, I & alpha; is the Riesz potential, s & ISIN; (0, 1), 2s < N & ISIN; N, & alpha; & ISIN; (0, N) and p & ISIN; (N+& alpha; N , N+& alpha; N-2s ). Via studying limiting profiles of ground states of the above problem, we establish the uniqueness and non-degeneracy of positive ground states as & alpha; is close to 0 and & alpha; is close to N ...
