Selected Topics in Partial Differential Equations
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
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.
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 70
Mathematics Computational Mathematics
IdentifiersURN: urn:nbn:se:uu:diva-145763ISBN: 978-91-506-2193-8OAI: oai:DiVA.org:uu-145763DiVA: diva2:398102
2011-03-31, Häggsalen, Lägerhyddsvägen 1, Uppsala, 09:15 (English)
Evans, William Desmond, Professor
Melgaard, Michael, Docent
I den tryckta boken har förlag felaktigt angivits som Acta Universitatis Upsaliensis.2011-03-102011-02-102011-10-25Bibliographically approved
List of papers