Uniqueness and existence of positive periodic solutions of functional differential equations

Jiaqi Xu; Chunyan Xue; Jiaqi Xu; Chunyan Xue

doi:10.3934/math.2023032

AIMS Mathematics

2023, Volume 8, Issue 1: 676-690. doi: 10.3934/math.2023032

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Research article

Uniqueness and existence of positive periodic solutions of functional differential equations

Jiaqi Xu ,
Chunyan Xue ^,

School of Applied Science, Beijing Information Science & Technology University, Beijing, 100192, China

Received: 22 May 2022 Revised: 04 September 2022 Accepted: 23 September 2022 Published: 09 October 2022
MSC : 34K13

In this paper, some new findings on the uniqueness and existence of positive periodic solutions to first-order functional differential equations are presented. These equations have wide applications in a variety of fields. The most important feature of our argument is that we use the theory of Hilbert's metric to prove the uniqueness of the positive periodic solution when $ q=-1 $ and $ -1 < q < 0 $. In addition, we also investigate the existence results of positive periodic solutions by applying a fixed point theorem for completely continuous maps in a cone. Two examples demonstrate our findings.
- functional differential equation,
- positive periodic solution,
- uniqueness and existence,
- Hilbert's metric,
- fixed point theorem
Citation: Jiaqi Xu, Chunyan Xue. Uniqueness and existence of positive periodic solutions of functional differential equations[J]. AIMS Mathematics, 2023, 8(1): 676-690. doi: 10.3934/math.2023032

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Abstract

In this paper, some new findings on the uniqueness and existence of positive periodic solutions to first-order functional differential equations are presented. These equations have wide applications in a variety of fields. The most important feature of our argument is that we use the theory of Hilbert's metric to prove the uniqueness of the positive periodic solution when $ q=-1 $ and $ -1 < q < 0 $. In addition, we also investigate the existence results of positive periodic solutions by applying a fixed point theorem for completely continuous maps in a cone. Two examples demonstrate our findings.

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