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The existence of equilibria of many-particle systems

Published online by Cambridge University Press:  26 May 2009

R. Stańczy
R. Stańczy
Affiliation:
Instytut Matematyczny, Uniwersytet Wrocławski, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland ([email protected])
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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
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 3 , June 2009 , pp. 623 - 631
Copyright
Copyright © Royal Society of Edinburgh 2009

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