Work

Normalized Ground States Satisfying the Pohozaev Identity for Fractional Choquard Equations

Year: 2026

Type: article

Abstract: 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.

Source: Symmetry

DOI: 10.3390/sym18040656

Author: Luyan Zhou

Institution: Henan University of Science and Technology

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funders: National Natural Science Foundation of China, Henan University of Science and Technology, Henan University