Dynamical system modeling fermionic limit

TL;DR

This paper proves the existence of multiple solutions to an elliptic equation modeling fermionic particles, using dynamical system methods and analyzing the limit as the Planck constant approaches zero.

Contribution

It introduces a novel approach by linking the elliptic problem to a nonautonomous dynamical system and analyzing the limit behavior for the Planck constant.

Findings

Multiple radial solutions are established for the limiting Planck constant.

Continuity of solutions with respect to the parameter is demonstrated.

The approach bridges elliptic equations and dynamical systems analysis.

Abstract

The existence of multiple radial solutions to the elliptic equation modeling fermionic cloud of interacting particles is proved for the limiting Planck constant and intermediate values of mass parameters. It is achieved by considering the related nonautonomous dynamical system for which the passage to the limit can be established due to the continuity of the solutions with respect to the parameter going to zero.