Copyright © 2009 M. Enstedt and M. Melgaard. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We establish existence of infinitely many distinct solutions to the semilinear elliptic Hartree-Fock equations for -electron Coulomb systems with quasirelativistic kinetic energy for the electron. Moreover, we prove existence of a ground state. The results are valid under the hypotheses that the total charge of nuclei is greater than and that is smaller than a critical charge . The proofs are based on a new application of the Fang-Ghoussoub critical point approach to multiple solutions on a noncompact Riemannian manifold, in combination with density operator techniques.