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

TL;DR

This paper investigates the existence and asymptotic behavior of ground states in a Hartree-Fock type system involving coupled Schrödinger equations with Coulomb interaction and nonlinearities, analyzing how solutions change with a parameter.

Contribution

It establishes the existence of both semitrivial and vectorial ground states and studies their asymptotic behavior as the parameter varies.

Findings

Existence of semitrivial ground states

Existence of vectorial ground states

Asymptotic analysis of solutions with respect to parameter β

Abstract

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