Dynamical system modeling fermionic limit

Dorota Bors, Robert Stańczy
2017 Discrete and continuous dynamical systems. Series B  
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. 2010 Mathematics Subject Classification. Primary: 35Q85, 70K05, 85A05; Secondary:
more » ... 15, 37N05. 45 46 DOROTA BORS AND ROBERT STAŃCZY The problem can be reduced, by appropriate substitution, to some dynamical 4. Appendix. Lemma 4.1. For simplified Fermi-Dirac model we have straightforward estimate Proof. Indeed, recall the formula R η (z) = (1/z + η/z 1−2/d ) −1 . Then z −1−2/d (z − R η (z)) = ηz 4/d z 4/d + ηz 6/d ≤ η.
doi:10.3934/dcdsb.2018004 fatcat:vyfbyb3b6vfglfgbnh3raekqaq