Existence of Infinitely Many Distinct Solutions to the Quasirelativistic Hartree-Fock Equations
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 h...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2009/651871 |
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| author | M. Enstedt M. Melgaard |
| author_facet | M. Enstedt M. Melgaard |
| author_sort | M. Enstedt |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-509d29d37403483a892fa5e3ee20866d |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-509d29d37403483a892fa5e3ee20866d2025-02-03T01:32:54ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252009-01-01200910.1155/2009/651871651871Existence of Infinitely Many Distinct Solutions to the Quasirelativistic Hartree-Fock EquationsM. Enstedt0M. Melgaard1Department of Mathematics, Uppsala University, 751 06 Uppsala, SwedenSchool of Mathematical Sciences, Dublin Institute of Technology, Dublin 8, IrelandWe 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.http://dx.doi.org/10.1155/2009/651871 |
| spellingShingle | M. Enstedt M. Melgaard Existence of Infinitely Many Distinct Solutions to the Quasirelativistic Hartree-Fock Equations International Journal of Mathematics and Mathematical Sciences |
| title | Existence of Infinitely Many Distinct Solutions to the Quasirelativistic Hartree-Fock Equations |
| title_full | Existence of Infinitely Many Distinct Solutions to the Quasirelativistic Hartree-Fock Equations |
| title_fullStr | Existence of Infinitely Many Distinct Solutions to the Quasirelativistic Hartree-Fock Equations |
| title_full_unstemmed | Existence of Infinitely Many Distinct Solutions to the Quasirelativistic Hartree-Fock Equations |
| title_short | Existence of Infinitely Many Distinct Solutions to the Quasirelativistic Hartree-Fock Equations |
| title_sort | existence of infinitely many distinct solutions to the quasirelativistic hartree fock equations |
| url | http://dx.doi.org/10.1155/2009/651871 |
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