On a Diffusive Logistic Equation

G. A. Afrouzi; K. J. Brown

doi:10.1006/jmaa.1998.6044

On a Diffusive Logistic Equation

G. A. Afrouzi, K. J. Brown

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Abstract

We study a reaction-diffusion version on all of R^Nof the logistic equation of population growth in which the birth rate depends on the spatial variable and may assume both positive and negative values. Our results which are obtained by the construction of sub- and supersolutions and the study of asymptotic properties of solutions show the interplay between the birth rate of the species and the extent of diffusion in determining the existence or nonexistence of nontrivial steady-state distributions of population. © 1998 Academic Press.

Original language	English
Pages (from-to)	326-339
Number of pages	14
Journal	Journal of Mathematical Analysis and Applications
Volume	225
Issue number	1
DOIs	https://doi.org/10.1006/jmaa.1998.6044
Publication status	Published - 1 Sep 1998

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AB - We study a reaction-diffusion version on all of RNof the logistic equation of population growth in which the birth rate depends on the spatial variable and may assume both positive and negative values. Our results which are obtained by the construction of sub- and supersolutions and the study of asymptotic properties of solutions show the interplay between the birth rate of the species and the extent of diffusion in determining the existence or nonexistence of nontrivial steady-state distributions of population. © 1998 Academic Press.

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DO - 10.1006/jmaa.1998.6044

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EP - 339

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

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On a Diffusive Logistic Equation

Abstract

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