In this paper, we are concerned with the stability for a model in the form of system of integro-partial differential equations, which governs the evolution of two competing age-structured populations. The age-specified environment is incorporated in the vital rates, which displays the hierarchy of ages. By a non-zero fixed-point result, we show the existence of positive equilibria. Some conditions for the stability of steady states are derived by means of semigroup method. Furthermore, numerical experiments are also presented.
The $C$-regularized semigroup method for partial differential equations with delays
