Steady states for a system describing self-gravitating Fermi-Dirac particles

Abstract

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.