Existence and Uniqueness of a Solution for a Four-Stage Age-Structured Population Dynamics Model With Spatial Diffusion for Desert Locusts

Abstract

We consider a linear system based on a population dynamics model dependent on age, space and nonlocal boundary conditions. Note that our population dynamics model is a four-step model with a second derivative with respect to the age variable and a second derivative with respect to the space variable. Population growth at each stage depends on time and space. We prove the uniqueness and existence of a positive solution by combining the Galerkin’s variational method and the Banach’s fixed point theorem.