Remarks on the nonlinear fractional Choquard equation

We analyze the following doubly nonlocal nonlinear elliptic problem: (Formula presented.) where N≥2, s∈(0,1), ω>0, (-Δ)s denotes the fractional Laplacian, Iα is the Riesz potential of order α∈(0,N), and F:R→R is a C1-nonlinearity of Berestycki-Lions type, exhibiting subcritical or critical growth in the sense of the Hardy-Littlewood-Sobolev inequality. By employing suitable variational techniques, we investigate the existence and qualitative properties of least energy solutions.