International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 651871, 20 pages
Research Article

Existence of Infinitely Many Distinct Solutions to the Quasirelativistic Hartree-Fock Equations

1Department of Mathematics, Uppsala University, 751 06 Uppsala, Sweden
2School of Mathematical Sciences, Dublin Institute of Technology, Dublin 8, Ireland

Received 18 March 2009; Revised 8 July 2009; Accepted 10 August 2009

Academic Editor: Irena Lasiecka

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 N-electron Coulomb systems with quasirelativistic kinetic energy α2Δxn+α4α2 for the nth electron. Moreover, we prove existence of a ground state. The results are valid under the hypotheses that the total charge Ztot of K nuclei is greater than N1 and that Ztot is smaller than a critical charge Zc. 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.