International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 651871, 20 pages
doi:10.1155/2009/651871
Existence of infinitely many distinct solutions to the quasirelativistic Hartree-Fock equations
M. Enstedt1
and M. Melgaard2
1Department of Mathematics, Uppsala University, 751 06 Uppsala, Sweden
2School of Mathematical Sciences, Dublin Institute of Technology, Dublin 8, Ireland
Abstract
We establish existence of infinitely many distinct solutions to the semilinear elliptic Hartree-Fock equations for N-electron Coulomb systems with quasirelativistic kinetic energy −α−2Δxn+α−4−α−2 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 N−1 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.