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Multiple solutions of Choquard type equations
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2010 (English)Report (Other academic)
Place, publisher, year, edition, pages
2010.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-145760OAI: oai:DiVA.org:uu-145760DiVA: diva2:396749
Available from: 2011-02-10 Created: 2011-02-10 Last updated: 2012-05-16Bibliographically 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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CiteExportLink to record
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  • apa
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Output format
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