On the generalized semi-relativistic Schr\"odinger-Poisson system in R^n

TL;DR

This paper investigates the semi-relativistic Schr"odinger-Poisson system in multiple dimensions, analyzing existence, behavior, and the non-relativistic limit as mass increases, with implications for understanding nonlocal interactions.

Contribution

It provides a rigorous analysis of the well-posedness and asymptotic behavior of solutions for the semi-relativistic Schr"odinger-Poisson system in R^n.

Findings

Established existence and uniqueness of solutions for a broad class of nonlocal interactions.

Analyzed the asymptotic behavior as mass tends to infinity, demonstrating a non-relativistic limit.

Provided insights into the impact of nonlocal interactions on solution dynamics.

Abstract

The Cauchy problem for the semi-relativistic Schr\"odinger-Poisson system of equations is studied in ${\mathbb R}^n$, $n\geq 1$, for a wide class of nonlocal interactions. Furthermore, the asymptotic behavior of the solution as the mass tends to infinity is rigorously discussed, which corresponds to a non-relativistic limit.