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Title: Unbounded Principal Eigenfunctions and the Logistic Equation on R^N
Contributor(s): Du, Yihong  (author); Dong, Wei (author)
Publication Date: 2003
DOI: 10.1017/S0004972700037229
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Abstract: We consider the logistic equation -∆u=a(x)u-b(x)u^p on all of R^N with possibly unbounded coefficients near infinity. We show that under suitable growth conditions of the coefficients, the behaviour of the positive solutions of the logistic equation can be largely determined. We also show that certain linear eigenvalue problems on all of R^N have principal eigenfunctions that become unbounded near infinity at an exponential rate. Using these results, we finally show that the logistic equation has unique positive solution under suitable growth restrictions for its coefficients.
Publication Type: Journal Article
Source of Publication: Bulletin of the Australian Mathematical Society, 67(3), p. 413-427
Publisher: Cambridge University Press
Place of Publication: Australia
ISSN: 0004-9727
Field of Research (FOR): 010109 Ordinary Differential Equations, Difference Equations and Dynamical Systems
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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