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Please use this identifier to cite or link to this item: https://hdl.handle.net/1959.11/2976
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dc.contributor.authorDancer, Edward Nen
dc.contributor.authorYan, Shusenen
dc.date.accessioned2009-11-09T16:28:00Z-
dc.date.issued2008-
dc.identifier.citationJournal of the London Mathematical Society, 78(3), p. 639-662en
dc.identifier.issn1469-7750en
dc.identifier.issn0024-6107en
dc.identifier.urihttps://hdl.handle.net/1959.11/2976-
dc.description.abstractWe prove that certain super-linear elliptic equations in two dimensions have many solutions when the diffusion is small. We find these solutions by constructing solutions with many sharp peaks. In three or more dimensions, this has already been proved by the authors in 'Comm. Partial Differential Equations' 30 (2005) 1331-1358. However, in two dimensions, the problem is much more difficult because there is no limit problem in the whole space. Therefore, the proof is quite different, though still a reduction argument. A direct consequence of this result is that we give a positive answer to the Lazer-McKenna conjecture for some typical nonlinearities in two dimensions.en
dc.languageenen
dc.publisherOxford University Pressen
dc.relation.ispartofJournal of the London Mathematical Societyen
dc.titleThe Lazer-McKenna conjecture and a free boundary problem in two dimensionsen
dc.typeJournal Articleen
dc.identifier.doi10.1112/jlms/jdn045en
dc.subject.keywordsStatistical Mechanics, Physical Combinatorics and Mathematical Aspects of Condensed Matteren
local.contributor.firstnameEdward Nen
local.contributor.firstnameShusenen
local.subject.for2008010506 Statistical Mechanics, Physical Combinatorics and Mathematical Aspects of Condensed Matteren
local.subject.seo2008970101 Expanding Knowledge in the Mathematical Sciencesen
local.profile.schoolAdministrationen
local.profile.schoolSchool of Science and Technologyen
local.profile.emailedancer@une.edu.auen
local.profile.emailsyan@une.edu.auen
local.output.categoryC1en
local.record.placeauen
local.record.institutionUniversity of New Englanden
local.identifier.epublicationsrecordpes:6725en
local.publisher.placeUnited Kingdomen
local.format.startpage639en
local.format.endpage662en
local.peerreviewedYesen
local.identifier.volume78en
local.identifier.issue3en
local.contributor.lastnameDanceren
local.contributor.lastnameYanen
dc.identifier.staffune-id:edanceren
dc.identifier.staffune-id:syanen
local.profile.roleauthoren
local.profile.roleauthoren
local.identifier.unepublicationidune:3055en
dc.identifier.academiclevelAcademicen
dc.identifier.academiclevelAcademicen
local.title.maintitleThe Lazer-McKenna conjecture and a free boundary problem in two dimensionsen
local.output.categorydescriptionC1 Refereed Article in a Scholarly Journalen
local.search.authorDancer, Edward Nen
local.search.authorYan, Shusenen
local.uneassociationUnknownen
local.identifier.wosid000260976000006en
local.year.published2008en
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