Dynamical system modeling fermionic limit

Dorota Bors; Robert Stańczy

doi:10.3934/dcdsb.2018004

Article Contents

2018, Volume 23, Issue 1: 45-55. Doi: 10.3934/dcdsb.2018004

This issue Previous Article Application of Mountain Pass Theorem to superlinear equations with fractional Laplacian controlled by distributed parameters and boundary data Next Article NLS-like equations in bounded domains: Parabolic approximation procedure

Dynamical system modeling fermionic limit

Dorota Bors^1, and
Robert Stańczy^2,

1.
Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Ƚódź, Poland
2.
Instytut Matematyczny, Uniwersytet Wrocławski, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Received: September 30, 2016

Revised: March 31, 2017

Published: November 2017

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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 value 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.

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Mathematics Subject Classification: Primary: 35Q85, 70K05, 85A05; Secondary: 34E15, 37N05.

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Figure 1. Left: the heteroclinic orbit joining the points $(0,0)$ and $(2,2)$ in the Maxwell-Boltzmann case. Right: the mass-density diagram.

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