Existence of normalized solutions for fractional coupled Hartree-Fock type system

2022/09/18 by Meng Li, Li, Meng
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2209.08537

openalex publication_date 2022/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the existence of solutions for the following fractional coupled Hartree-Fock type system \\beginaligned amp;(-Δ)^s u+V₁(x)u+λ₁u=μ₁(I_α⋆ |u|^p)|u|^p-2u+β(I_α⋆ |v|^r)|u|^r-2u
amp;(-Δ)^s v+V₂(x)v+λ₂v=μ₂(I_α⋆ |v|^q)|v|^q-2v+β(I_α⋆ |u|^r)|v|^r-2v \endaligned .~ x∈ℝ^N, under the constraint ∫_ℝ^N|u|²=a²,~∫_ℝ^N|v|²=b². where s∈(0,1),~N≥3,~μ₁>0,~μ₂>0,~β>0,~α∈(0,N),~1+\fracαN

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