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

TL;DR

This paper proves the existence and describes properties of solutions for a class of Hartree-Fock systems with logarithmic interactions in two dimensions, highlighting how solutions depend on the interaction parameter.

Contribution

It introduces a Nehari-Pohozaev manifold approach to establish existence, regularity, and asymptotic behavior of solutions for Hartree-Fock systems with logarithmic interactions.

Findings

Existence of nontrivial solutions depending on interaction parameter

Solutions can be vector or semitrivial ground states

Asymptotic behavior characterized with respect to parameter eta>0

Abstract

We establish the existence and qualitative properties of nontrivial solutions for a class of Hartree-Fock type systems defined over the whole space $\mathbb{R}^2$. By introducing a suitable Nehari-Pohozaev manifold, we prove the existence, regularity and we describe the asymptotic behavior of solutions with respect to the interaction parameter $\beta > 0$. In particular, we show that the system admits either a vector ground state or a semitrivial ground state solution, depending on the magnitude of $\beta$.