Existence of normalized solutions to Choquard equation with general mixed nonlinearities

Abstract

We study the existence of normalized solutions to the following Choquard equation with F being a Berestycki-Lions type function { − Δ u + λu = ( I α ∗ F ( u ) ) f ( u ) , in R N , ∫ R N | u | 2 d x = ρ 2 , where N ≥ 3 , 0 $ ]]> ρ > 0 is assigned, α ∈ ( 0 , N ) , I α is the Riesz potential, and λ ∈ R is an unknown parameter that appears as a Lagrange multiplier. Here, the general nonlinearity F contains the L 2 -subcritical and L 2 -supercritical mixed case, the Hardy-Littlewood-Sobolev lower critical and upper critical cases.