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Selected Topics in Partial Differential EquationsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2011 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### 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: urn:nbn:se:uu:diva-145763ISBN: 978-91-506-2193-8 (print)OAI: oai:DiVA.org:uu-145763DiVA: diva2:398102
##### Public defence

2011-03-31, Häggsalen, Lägerhyddsvägen 1, Uppsala, 09:15 (English)
##### Opponent

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt469",{id:"formSmash:j_idt469",widgetVar:"widget_formSmash_j_idt469",multiple:true});
##### Supervisors

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt476",{id:"formSmash:j_idt476",widgetVar:"widget_formSmash_j_idt476",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt482",{id:"formSmash:j_idt482",widgetVar:"widget_formSmash_j_idt482",multiple:true});
##### 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
##### List of papers

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.

1. Abstract criteria for multiple solutions to nonlinear coupled equations involving magnetic Schrödinger operators$(function(){PrimeFaces.cw("OverlayPanel","overlay396747",{id:"formSmash:j_idt523:0:j_idt527",widgetVar:"overlay396747",target:"formSmash:j_idt523:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Existence of infinitely many solutions to the quasi-relativistic Hartree-Fock equations$(function(){PrimeFaces.cw("OverlayPanel","overlay396750",{id:"formSmash:j_idt523:1:j_idt527",widgetVar:"overlay396750",target:"formSmash:j_idt523:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Existence of a solution to Hartree-Fock equations with decreasing magnetic fields$(function(){PrimeFaces.cw("OverlayPanel","overlay396751",{id:"formSmash:j_idt523:2:j_idt527",widgetVar:"overlay396751",target:"formSmash:j_idt523:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. Multiple solutions of Choquard type equations$(function(){PrimeFaces.cw("OverlayPanel","overlay396749",{id:"formSmash:j_idt523:3:j_idt527",widgetVar:"overlay396749",target:"formSmash:j_idt523:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

5. Weighted spectral gap for magnetic Schrödinger operators with a potential term$(function(){PrimeFaces.cw("OverlayPanel","overlay304117",{id:"formSmash:j_idt523:4:j_idt527",widgetVar:"overlay304117",target:"formSmash:j_idt523:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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