Hartree-Fock type systems: existence of ground states and asymptotic behavior

2020/08/07 by P. d'Avenia, d'Avenia, P., L. A. Maia +3 · 1 citation
Mathematics · Physics and Astronomy · #35J10 #35J50 #35Q92 #35R09 #81V55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2008.03191

openalex publication_date 2020/08/07 · openalex created_date 2022/10/15 · openalex updated_date 2026/07/28

Abstract

In this paper we consider an Hartree-Fock type system made by two Schrödinger equations in presence of a Coulomb interacting term and a cooperative pure power and subcritical nonlinearity, driven by a suitable parameter β≥ 0. We show the existence of semitrivial and vectorial ground states solutions depending on the parameters involved. The asymptotic behavior with respect to the parameter β of these solutions is also studied.

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• A class of Hartree-Fock systems with null mass via Nehari-Pohozaev with logarithmic interactions

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