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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:doi:10.3934/dcdsb.2018004 fatcat:vyfbyb3b6vfglfgbnh3raekqaq