Vectorial ground state solutions for a class of Hartree-Fock type systems with the double coupled feature

2023/09/27 by Juntao Sun, Sun, Juntao, Tsung‐fang Wu +1
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nuclear physics research studies #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2309.15618

openalex publication_date 2023/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the Hartree-Fock type system as follows: \ -Δu+u+λϕ_u,vu=\vert u\vert ^p-2u+β\vert v\vert ^(p)/(2)\vert u\vert ^{(p)/(2)% -2}u · amp; in ℝ³,
-Δv+v+λϕ_u,vv=\vert v\vert ^p-2v+β\vert u\vert ^(p)/(2)\vert v\vert ^{(p)/(2)% -2}v · amp; in ℝ³,%% .% where ϕ_u,v(x)=∫_ℝ³\fracu²(y)+v²( y) |x-y|dy, the parameters λ,β>0 and 2

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