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The existence of equilibria of many-particle systems

Published online by Cambridge University Press:  26 May 2009

R. Stańczy
Affiliation:
Instytut Matematyczny, Uniwersytet Wrocławski, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland (stanczr@math.uni.wroc.pl)

Abstract

In this paper we obtain the existence of a radial solution for some elliptic non-local problem with constraints. The problem arises from some mean field equation which models, among other things, a system of self-gravitating particles when one looks for its stationary solutions. We include the cases of Maxwell—Boltzmann, Fermi—Dirac and polytropic statistics.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2009

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