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Topics in Nonlinear Elliptic 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

Stockholm: Department of Mathematics, Stockholm University , 2011. , 125 p.
##### Keyword [en]

Concentration-compactness principle, critical Sobolev exponent, symmetric solutions of elliptic equations, degenerate elliptic equation, Nehari manifold, Caffarelli-Kohn-Nirenberg inequality, infinitely many solutions
##### National Category

Mathematics
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:su:diva-56727ISBN: 978-91-7447-279-0 (print)OAI: oai:DiVA.org:su-56727DiVA: diva2:412818
##### Public defence

2011-06-01, sal 14, hus 5, Kräftriket, Roslagsvägen 101, Stockholm, 13:00 (English)
##### Opponent

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##### Supervisors

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#####

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##### Note

##### List of papers

In this thesis we examine the existence of solutions to nonlinear elliptic partial differential equations via variational methods.

In Paper I we consider the existence of constrained minimizers which correspond to solutions of equations involving the iterated Laplacian, the iterated p-Laplacian and the critical Sobolev exponent. Particular attention is paid to problems with symmetries.

In Paper II we work on singular elliptic problems related to the Caffarelli-Kohn-Nirenberg-Lin inequality, which generalizes the Sobolev inequality. We prove the existence of solutions which break the symmetry of the underlying problem and have a prescribed number of nodal domains.

In Paper III we consider a different class of weighted problems related to the Caffarelli-Kohn-Nirenberg-Lin inequality. We establish the existence of at least one nontrivial solution. In the case $p=2$ (the iterated Laplacian) we show that there are infinitely many solutions.

In Paper IV we extend the results of Paper III concerning the existence of infinitely many solutions to the case $p\neq 2$ (the iterated p-Laplacian) and to a larger class of weights.

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 1: Manuscript. Paper 2: Manuscript. Paper 3: Submitted.

Available from: 2011-05-11 Created: 2011-04-26 Last updated: 2013-04-02Bibliographically approved1. Infinitely many solutions for some singular elliptic problems$(function(){PrimeFaces.cw("OverlayPanel","overlay566615",{id:"formSmash:j_idt498:0:j_idt502",widgetVar:"overlay566615",target:"formSmash:j_idt498:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Sign-changing and symmetry-breaking solutions to singular problems$(function(){PrimeFaces.cw("OverlayPanel","overlay575189",{id:"formSmash:j_idt498:1:j_idt502",widgetVar:"overlay575189",target:"formSmash:j_idt498:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Higher order singular problems of Caffarelli-Kohn-Nirenberg-Lin type$(function(){PrimeFaces.cw("OverlayPanel","overlay408691",{id:"formSmash:j_idt498:2:j_idt502",widgetVar:"overlay408691",target:"formSmash:j_idt498:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. Minimizers and symmetric minimizers for problems with critical Sobolev exponent$(function(){PrimeFaces.cw("OverlayPanel","overlay411579",{id:"formSmash:j_idt498:3:j_idt502",widgetVar:"overlay411579",target:"formSmash:j_idt498:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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