The sub-supersolution method for an evolutionary reaction-diffusion age-dependent problem

Abstract

In this work, we analyze a nonlinear population-dynamics model with age dependence and spatial diffusion, and where we are assuming the influence of a reaction term. Using a sub-supersolution method we derive existence and uniqueness results. We apply this method to study the existence and uniqueness of a positive solution of a generalized logistic and of a Holling-Tanner-type age-dependent model as well as its large-time behaviour.