Normalized solutions of NLS equations with mixed nonlocal nonlinearities

We study the existence and nonexistence of normalized solutions for the nonlinear Schrödinger equation with mixed nonlocal nonlinearities: − Δ u = λ u + μ ( I α ∗ ∣ u ∣ p ) ∣ u ∣ p − 2 u + ( I α ∗ ∣ u ∣ q ) ∣ u ∣ q − 2 u in R N , ∫ R N ∣ u ∣ 2 d x = c , \{{array}{ll}-Δ u=λ u+μ ({I}α {| u| }ᵖ){| u| }ᵖ⁻²u+({I}α {| u| }q){| u| }q-2u& {0.1em}in{0.1em}{0.33em}{{R}}N,\\ { ∫ }_{{{R}}N}{| u| }²{d}x=c,& {array}. where