Normalized solutions for the Choquard equations with critical nonlinearities

This study is concerned with the existence of normalized solutions for the Choquard equations with critical nonlinearities − Δ u + λ u = f ( u ) + ( I α ∗ ∣ u ∣ 2 α * ) ∣ u ∣ 2 α * − 2 u , in R N , ∫ R N ∣ u ∣ 2 d x = a 2 , \left\{\begin{array}{l}-\Delta u+\lambda u=f\left(u)+\left({I}_{\alpha }\ast {| u| }^{{2}_{\alpha }^{* }}){| u| }^{{2}_{\alpha }^{* }-2}u,\hspace{1em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.