Global Dynamics of Generalized Logistic Equations

Abstract

We consider a parameter dependent parabolic logistic population model with diffusion and degenerate logistic term allowing for refuges for the population. The aim of the paper is to remove quite restrictive geometric and smoothness conditions on the refuge used in the existing literature. The key is a new simplified construction of a supersolution that does not make use of any regularity condition of the refuge. At the same time we also simplify other arguments commonly used in the literature.