Solitary waves for the nonlinear Schr\"odinger-Poisson system with positron-electron interaction

TL;DR

This paper investigates the existence of positive solutions in a nonlinear Schrödinger-Poisson system modeling positron-electron interactions, focusing on parameter conditions that determine solution existence.

Contribution

It provides a new analysis of positive solutions for the nonlinear Schrödinger-Poisson system derived from Maxwell-Klein-Gordon equations, highlighting parameter-dependent existence results.

Findings

Existence of positive solutions depends on parameters p and μ_{ij}.

Conditions for nonexistence of solutions are characterized.

The study bridges nonlinear Schrödinger-Poisson systems with physical positron-electron models.

Abstract

In this paper, we study the existence of positive solutions to the nonlinear elliptic system, which is derived from taking the nonrelativistic limit of the nonlinear Maxwell-Klein-Gordon equations under the decomposition of waves functions into positron and electron parts. We characterize the existence and nonexistence of positive vector solutions, depending on parameters $p$ and $\mu_{ij}$.