Normalized ground states for a Hardy–Littlewood–Sobolev upper critical Schrödinger equation with double Choquard type nonlinear terms. (April 2023) - Chen, Jianqing; Chen, Zhewen
Abstract: In this paper, we study the existence of normalized ground states for a Hardy–Littlewood–Sobolev upper critical Schrödinger equation with double Choquard type nonlinear terms − Δ u = λ u + μ ( I α ∗ | u | p ) | u | p − 2 u + ( I α ∗ | u | 2 α ∗ ) | u | 2 α ∗ − 2 u in R N, ∫ R N | u | 2 = a, where N ≥ 3, μ > 0, N + α N < p < N + α + 2 N, α ∈ ( 0, N ), I α is the Riesz potential. We show that the associated energy functional admits a normalized ground state, which is a real valued, positive, radially symmetric, radially non-increasing function.