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

Keywords:

Fermi-Dirac particles