Existence of infinitely many distinct solutions to the quasirelativistic Hartree-Fock equations
type: Item
instance of: scholarly article
title: Existence of infinitely many distinct solutions to the quasirelativistic Hartree-Fock equations
zbMATH Open document ID: 1181.35288
DOI: 10.1155/2009/651871
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2009-11-10T00:00:00Z
full work available at URL: https://eudml.org/doc/45734
review text: Summary: We establish existence of infinitely many distinct solutions to the semilinear elliptic Hartree-Fock equations for \(N\)-electron Coulomb systems with quasirelativistic kinetic energy \(\sqrt{-\alpha^{-2}\Delta _{x_{n}}+\alpha ^{ - 4} - \alpha^{ - 2}}\) for the \(N\)th electron. Moreover, we prove existence of a ground state. The results are valid under the hypotheses that the total charge \(Z_{\text{tot}}\) of \(K\) nuclei is greater than \(N - 1\) and that \(Z_{\text{tot}}\) is smaller than a critical charge \(Z_{c}\). 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.
Mathematics Subject Classification ID: 35Q75
Mathematics Subject Classification ID: 35J61
Mathematics Subject Classification ID: 35A15
Mathematics Subject Classification ID: 58J60
Mathematics Subject Classification ID: 82B21
zbMATH DE Number: 5627900
zbMATH Keywords: \(N\)-electron Coulomb system
zbMATH Keywords: critical point approach
zbMATH Keywords: density operator
author: M. Enstedt
author: M. Melgaard
Wikidata QID: Q58648491
MaRDI profile type: Publication
OpenAlex ID: W2020421103
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DBLP publication ID: journals/ijmmsc/EnstedtM09
description: scientific article; zbMATH DE number 5627900