Normalized Ground States Satisfying the Pohozaev Identity for Fractional Choquard Equations

This paper is devoted to the study of the following fractional Choquard equation with prescribed L2 norm: (−Δ)su+μu=Iα*F(u)F′(u)inRN,∥u∥L2(RN)=a, where N≥2, s∈(0,1), Iα is the Riesz potential with α∈(0,N), and F∈C1(R,R) satisfies the general Berestycki–Lions-type assumptions. Here, the parameter μ∈R will arise as a Lagrange multiplier. In the L2-subcritical case, we establish the existence of normalized ground states in Hs(RN) by applying minimax arguments to the Lagrange formulation and using the concentration-compactness principle to restore compactness. Moreover, we show that the normalized ground states constructed here additionally satisfy the Pohozaev identity. This result is noteworthy, since it remains an open question as to whether general solutions of fractional Choquard equations satisfy the Pohozaev identity.