Positive solutions for diffusive Logistic equation with refuge

Advances in Nonlinear Analysis

article

Jian-Wen Sun¹ 

[1] School of Mathematics and Statistics, Lanzhou University;Institute for Mathematical Sciences, Renmin University of China

关键词: Reaction-diffusion;    Positive solution;    Profile;   

DOI  :  10.1515/anona-2020-0036

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

In this paper, we study the stationary solutions of the Logistic equation ut=D[u]+λu−[b(x)+ε]up in Ω $$\begin{array}{} \displaystyle u_t=\mathcal {D}[u]+\lambda u-[b(x)+\varepsilon]u^p \text{ in }{\it\Omega} \end{array}$$ with Dirichlet boundary condition, here ? is a diffusion operator and ε > 0, p > 1. The weight function b ( x ) is nonnegative and vanishes in a smooth subdomain Ω 0 of Ω . We investigate the asymptotic profiles of positive stationary solutions with the critical value λ when ε is sufficiently small. We find that the profiles are different between nonlocal and classical diffusion equations.

【 授权许可】

CC BY