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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

In 1954 Nicholson [

Now, Nicholson’s blowflies model and its various analogous equations have attracted more and more attention. There is large literature on this topic. Recently, the study on Nicholson’s blowflies type systems has attracted much attention (cf. [

Stimulated by the above works, in this paper, we consider the following discrete Nicholson’s blowflies type system:

In fact, there are seldom results concerning the existence of

Next, let us recall the Leggett-Williams fixed point theorem, which will be used in the proof of our main results.

Let

A nonnegative continuous functional

Letting

Let

Throughout the rest of this paper, we denote by

To study the existence of multiple periodic solutions for system (

To note that the existence of periodic solutions for system (

Let

We first present some basic results about

For all

One can show (i) and (ii) by some direct calculations and noting that

By using Lemma

A function

Let

Now, we introduce a set

Assume that

There exist two constants

There exists a constant

Firstly, by (H0) and noting that

Let

Now, we show that

Let

In addition, for every

It remains to verify that condition (iii) of Lemma

Then, by Lemma

Now, we apply Theorem

Assume that

We only need to verify that all the assumptions of Theorem

It remains to verify (H2). For all

Next, we give a concrete example for Nicholson’s blowflies type system (

Let

The authors declare that there is no conflict of interests regarding the publication of this paper.

The authors are grateful to the referees for valuable suggestions and comments. Hui-Sheng Ding acknowledges support from the NSF of China (11101192), the Program for Cultivating Young Scientist of Jiangxi Province (20133BCB23009), and the NSF of Jiangxi Province.