Du, Yihong; Dong, Wei

Author(s)

Du, Yihong

Dong, Wei

Publication Date

2003

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.

Citation

Bulletin of the Australian Mathematical Society, 67(3), p. 413-427

ISSN

0004-9727

Link

https://hdl.handle.net/1959.11/3464

Publisher

Cambridge University Press

Title

Unbounded Principal Eigenfunctions and the Logistic Equation on R^N

Type of document

Journal Article

Entity Type

Publication

Author(s)	Du, Yihong Dong, Wei
Publication Date	2003
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.
Citation	Bulletin of the Australian Mathematical Society, 67(3), p. 413-427
ISSN	0004-9727
Link	https://hdl.handle.net/1959.11/3464
Publisher	Cambridge University Press
Title	Unbounded Principal Eigenfunctions and the Logistic Equation on R^N
Type of document	Journal Article
Entity Type	Publication

Unbounded Principal Eigenfunctions and the Logistic Equation on R^N

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