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Asymptotic profiles for positive solutions of diffusive logistic equations

Published online by Cambridge University Press:  15 February 2023

Jian-Wen Sun
School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, P.R. China (
Peng-Fei Fang
School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, P.R. China (


In this paper, we study the asymptotic profiles of positive solutions for diffusive logistic equations. The aim is to study the sharp effect of linear growth and nonlinear function. Both the classical reaction-diffusion equation and nonlocal dispersal equation are investigated. Our main results reveal that the linear and nonlinear parts of reaction term play quite different roles in the study of positive solutions.

Research Article
Copyright © The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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