Diffusive logistic equations in population dynamics

Abstract

The purpose of this paper is to prove an existence and uniqueness theorem of positive solutions of diffusive logistic equations with indefinite weights, which model population dynamics in environments with strong spatial heterogeneity. We prove that the most favorable situations will occur if there is a relatively large favorable region (with good resources and without crowding effects) located some distance away from the boundary of the environment. Moreover we discuss the stability properties for positive steady states.