Document Type



This item is available under a Creative Commons License for non-commercial use only


1.1 MATHMATICS, Pure mathematics, Applied mathematics, 1.3 PHYSICAL SCIENCES, Atomic, Molecular and Chemical Physics

Publication Details

Nonlinear Analysis: theory, methods, and applications 75 (2012), 384--404.


We establish existence of infinitely many distinct solutions to the multi-configurative Hartree-Fock type equations for N-electron Coulomb systems with quasi-relativistic kinetic energy for the n th electron. Finitely many of the solutions are interpreted as excited states of the molecule. Moreover, we prove existence of a ground state. The results are valid under the hypotheses that the total charge Z of K nuclei is greater than N-1 and that Z is smaller than a critical charge. The proofs are based on a new application of the Lions-Fang-Ghoussoub critical point approach to nonminimal solutions on a complete analytic Hilbert-Riemann manifold.