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Abstract criteria for multiple solutions to nonlinear coupled equations involving magnetic Schrödinger operators
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
Dublin Institute of Technology. (School of Mathematical Sciences)
2012 (English)In: Electronic Journal of Differential Equations, ISSN 1550-6150, E-ISSN 1072-6691, Vol. 253, no 6, 1729-1743 p.Article in journal (Refereed) Published
Abstract [en]

We consider a system of nonlinear coupled equations involving magnetic Schrodinger operators and general potentials. We provide the criteria for the existence of multiple solutions to these equations. As special cases we get the classical results on existence of infinitely many distinct solutions within Hartree and Hartree-Fock theory of atoms and molecules subject to an external magnetic fields. We also extend recent results within this theory, including Coulomb system with a constant magnetic field, a decreasing magnetic field and a "physically measurable" magnetic field.

Place, publisher, year, edition, pages
2012. Vol. 253, no 6, 1729-1743 p.
Keyword [en]
Nonlinear equations, Hartree-Fock model, Magnetic fields, Excited states, Ground state, Critical point theory
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-145759DOI: 10.1016/j.jde.2012.05.025ISI: 000306718400004OAI: oai:DiVA.org:uu-145759DiVA: diva2:396747
Available from: 2011-02-10 Created: 2011-02-10 Last updated: 2017-12-11Bibliographically approved
In thesis
1. Selected Topics in Partial Differential Equations
Open this publication in new window or tab >>Selected Topics in Partial Differential Equations
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This Ph.D. thesis consists of five papers and an introduction to the main topics of the thesis. In Paper I we give an abstract criteria for existence of multiple solutions to nonlinear coupled equations involving magnetic Schrödinger operators. In paper II we establish existence of infinitely many solutions to the quasirelativistic Hartree-Fock equations for Coulomb systems along with properties of the solutions. In Paper III we establish existence of a ground state to the magnetic Hartree-Fock equations. In Paper IV we study the Choquard equation with general potentials (including quasirelativistic and magnetic versions of the equation) and establish existence of multiple solutions. In Paper V we prove that, under some assumptions on its nonmagnetic counterpart, a magnetic Schrödinger operator admits a representation with a positive Lagrange density and we derive consequences of this property.

Place, publisher, year, edition, pages
Uppsala: Department of Mathematics, 2011. x, 14 p.
Series
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 70
National Category
Mathematics Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-145763 (URN)978-91-506-2193-8 (ISBN)
Public defence
2011-03-31, Häggsalen, Lägerhyddsvägen 1, Uppsala, 09:15 (English)
Opponent
Supervisors
Note
I den tryckta boken har förlag felaktigt angivits som Acta Universitatis Upsaliensis.Available from: 2011-03-10 Created: 2011-02-10 Last updated: 2011-10-25Bibliographically approved

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Melgaard, Michael

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