Asymptotic behaviors of normalized solutions for a class of Choquard equations

In this paper, we consider the following Choquard equations with double nonlocal nonlinearities: −Δu=λu+μ(Iα∗|u|p)|u|p−2u+(Iβ∗|u|N+βN−2)|u|N+βN−2−2uinRN,u∈H1(RN),∫RN|u|2=c2,where N≥5, N+αN0, Iα and Iβ are the Riesz potentials with α, β ∈(0,N) and the frequency λ∈R is unknown and appears as Lagrange multiplier. In Ye et al. (2022), Yang and his co-authors have proved the existence of ground states and mountain-pass type solutions under different assumptions. In this paper, we will prove the asymptotic behaviors of ground states and mountain-pass solutions as μ→0 (or c→0).