# American Institute of Mathematical Sciences

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January  2018, 23(1): 45-55. doi: 10.3934/dcdsb.2018004

## Dynamical system modeling fermionic limit

 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  October 2016 Revised  April 2017 Published  January 2018

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.

Citation: Dorota Bors, Robert Stańczy. Dynamical system modeling fermionic limit. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 45-55. doi: 10.3934/dcdsb.2018004
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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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