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This paper is devoted to multiplicity results of solutions to nonlocalelliptic equations modeling gravitating systems. By considering the case ofFermi-Dirac statistics as a singular perturbation of Maxwell-Boltzmann one, weare able to produce multiplicity results. Our method is based on cumulated massdensities and a logarithmic change of coordinates that allows us to describethe set of all solutions by a non-autonomous perturbation of an autonomousdynamical system. This has interesting consequences in terms of bifurcationdiagrams, which are illustrated by a some numerical computations. Morespecifically, we study a model based on the Fermi function as well as asimplified one for which estimates are easier to establish. The main difficultycomes from the fact that the mass enters in the equation as a parameter whichmakes the whole problem non-local.

Bifurcation diagrams and multiplicity for nonlocal elliptic equations modeling gravitating systems based on Fermi-Dirac statistics