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arXiv · 1309.1930

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

Jean Dolbeault·Robert Stanczy
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Abstract

This paper is devoted to multiplicity results of solutions to nonlocal elliptic equations modeling gravitating systems. By considering the case of Fermi-Dirac statistics as a singular perturbation of Maxwell-Boltzmann one, we are able to produce multiplicity results. Our method is based on cumulated mass densities and a logarithmic change of coordinates that allows us to describe the set of all solutions by a non-autonomous perturbation of an autonomous dynamical system. This has interesting consequences in terms of bifurcation diagrams, which are illustrated by a some numerical computations. More specifically, we study a model based on the Fermi function as well as a simplified one for which estimates are easier to establish. The main difficulty comes from the fact that the mass enters in the equation as a parameter which makes the whole problem non-local.

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Jean Dolbeault, Robert Stanczy. 2014-01-29. Bifurcation diagrams and multiplicity for nonlocal elliptic equations modeling gravitating systems based on Fermi-Dirac statistics. https://arxiv.org/abs/1309.1930

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