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

M. Enstedt and M. Melgaard

International Journal of Mathematics and Mathematical Sciences, 2009, vol. 2009, 1-20

Abstract:

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.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:651871

DOI: 10.1155/2009/651871

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