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

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  • M. Enstedt
  • M. Melgaard

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.

Suggested Citation

  • M. Enstedt & M. Melgaard, 2009. "Existence of Infinitely Many Distinct Solutions to the Quasirelativistic Hartree-Fock Equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2009, pages 1-20, September.
    • Handle: RePEc:hin:jijmms:651871
    DOI: 10.1155/2009/651871
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