In this talk, I focus on the following doubly nonlocal nonlinear elliptic problem:

((−∆ + m2)^s)u + ωu = (Iα ∗ F(u))F'(u) in R^N ,
u ∈ H^s(R^N ),
where N ≥ 2, s ∈ (0, 1), m > 0, ω > −m^2s
, (−∆ + m2)^s denotes the fractional
relativistic Schrödinger operator, I_α is the Riesz potential of order α ∈ (0,N),
and F : R → R is a C1-nonlinearity of Berestycki-Lions type. By employing suitable variational methods, I discuss the existence of least energy solutions.
I also analyze the regularity, decay, sign, and symmetry properties of these
solutions.