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Title: The Lazer-McKenna conjecture and a free boundary problem in two dimensions
Contributor(s): Dancer, Edward N  (author); Yan, Shusen  (author)
Publication Date: 2008
DOI: 10.1112/jlms/jdn045
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Abstract: We 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.
Publication Type: Journal Article
Source of Publication: Journal of London Mathematical Society, 78(3), p. 639-662
Publisher: Oxford University Press
Place of Publication: Oxford, United Kingdom
ISSN: 0024-6107
Field of Research (FOR): 010506 Statistical Mechanics, Physical Combinatorics and Mathematical Aspects of Condensed Matter
Socio-Economic Outcome Codes: 970101 Expanding Knowledge in the Mathematical Sciences
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
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Appears in Collections:Journal Article
School of Science and Technology

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