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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.
Enstedt,, M. & Melgaard, M. (2009). Existence of infinitely many distinct solutions to the quasi-relativistic Hartree-Fock equations. International Journal of Mathematics and Mathematical Sciences, vol. 2009, Article ID 651871. doi:10.1155/2009/651871
Science Foundation Ireland Stokes Award