Refuge versus dispersion in the logistic equation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:262

Article

Cintra, W.¹  Morales-Rodrigo, C.²  Suarez, A.² 

[1] Fed Univ Para, Fac Matemat, BR-66705110 Belem, Para, Brazil

[2] Univ Seville, Fac Matemat, Dept Ecuac Diferenciales & Anal Numer, Calle Tarfia S-N, Seville, Spain

关键词: Non-linear diffusion;    Bifurcation;    Sub-supersolution method;    Large solutions;    Population dynamics;   

DOI  :  10.1016/j.jde.2017.02.012

来源: Elsevier

【 摘 要 】

In this paper we consider a logistic equation with nonlinear diffusion arising in population dynamics. In this model, there exists a refuge where the species grows following a Malthusian law and, in addition, there exists also a non-linear diffusion representing a repulsive dispersion of the species. We prove existence and uniqueness of positive solution and study the behavior of this solution with respect to the parameter lambda, the growth rate of the species. Mainly, we use bifurcation techniques, the sub-supersolution method and a construction of appropriate large solutions. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free