Multiple Periodic Solutions for Discrete Nicholson’s Blowflies Type System

Abstract

This paper is concerned with the existence of multiple periodic solutions for discrete Nicholson’s blowflies type system. By using the Leggett-Williams fixed point theorem, we obtain the existence of three nonnegative periodic solutions for discrete Nicholson’s blowflies type system. In order to show that, we first establish the existence of three nonnegative periodic solutions for the $n$-dimensional functional difference system $y\left(k+1\right)=A\left(k\right)y\left(k\right)+f\left(k, y\left(k-\tau \right)\right), k\in \mathbb{Z}$, where $A\left(k\right)$ is not assumed to be diagonal as in some earlier results. In addition, a concrete example is also given to illustrate our results.