We analyze the following doubly nonlocal nonlinear elliptic problem: \(\begin{aligned} \left\{ \begin{array}{ll} (-\varDelta )^{s}u+\omega u=(I_{\alpha }*F(u)) F'(u) \text{ in } \mathbb {R}^{N}, \\ u\in H^{s}(\mathbb {R}^{N}), \end{array} \right. \end{aligned}\) where \(N\ge 2\) , \(s\in (0, 1)\) , \(\omega >0\) , \((-\varDelta )^{s}\) denotes the fractional Laplacian, \(I_{\alpha }\) is the Riesz potential of order \(\alpha \in (0, N)\) , and \(F:\mathbb {R}\rightarrow \mathbb {R}\) is a \(C^1\) -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.
