This paper investigates the existence of normalized solutions to the nonlinear fractional Choquard equation: (-Δ) ˢ u+V (x) u=λu+f (x) (I_α* (f|u|q) ) |u|^q-2 u+g (x) (I_α* (g|u|ᵖ) ) |u|^p-2 u, x RN subject to the mass constraint ₑ₍|u|² d x=a>0, where N>2 s, s (0, 1), α (0, N), and N+αN q<p N+α+2 sN. Here, the parameter λ R appears as an unknown Lagrange multiplier associated with the normalization condition. By employing variational methods under appropriate assumptions on the potentials V (x), f (x), and g (x), we establish several existence results for normalized solutions.
Chen et al. (Thu,) studied this question.