Semiclassical limit for Schr\"odinger equations with magnetic field and Hartree-type nonlinearities

TL;DR

This paper investigates the semi-classical behavior of Schrödinger equations with magnetic fields and Hartree nonlinearities, revealing solutions that concentrate around electric potential minima.

Contribution

It establishes the existence of multiple concentration solutions in the semi-classical limit for Schrödinger equations with magnetic and non-local Hartree nonlinearities.

Findings

Solutions concentrate around electric potential minima

Multiple concentration regions are identified

Semi-classical limit behavior is characterized

Abstract

The semi-classical regime of standing wave solutions of a Schr\"odinger equation in presence of non-constant electric and magnetic potentials is studied in the case of non-local nonlinearities of Hartree type. It is show that there exists a family of solutions having multiple concentration regions which are located around the minimum points of the electric potential.