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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||Handle Link:||https://hdl.handle.net/1959.11/3464||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||Statistics to Oct 2018:||Visitors: 177
|Appears in Collections:||Journal Article|
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