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Steady states for a system describing self-gravitating Fermi-Dirac particles. (English) Zbl 1212.35132

Summary: In this paper we obtain existence, nonexistence, and multiplicity results for the Dirichlet boundary-value problem \(-\Delta u=f_\alpha (u+c)\) in a bounded domain \(\Omega \subset \mathbb R^d\), with a nonlocal condition \(\int _\Omega f_\alpha (u+c)=M\). The solutions of this BVP are steady states for some evolution system describing self-gravitating Fermi-Dirac particles.

MSC:

35J60 Nonlinear elliptic equations
35J65 Nonlinear boundary value problems for linear elliptic equations
47J05 Equations involving nonlinear operators (general)
47J30 Variational methods involving nonlinear operators
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