Asymptotic behavior of some differential inequalities with mixed delays on time scales and their applications

Bingxian Wang; Mei Xu; Bingxian Wang; Mei Xu

doi:10.3934/math.2024797

AIMS Mathematics

2024, Volume 9, Issue 6: 16453-16467. doi: 10.3934/math.2024797

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Asymptotic behavior of some differential inequalities with mixed delays on time scales and their applications

Bingxian Wang ,
Mei Xu ^,

School of Mathematics and Statistics, Huaiyin Normal University, Huaian, Jiangsu, 223300, China

Received: 13 March 2024 Revised: 18 April 2024 Accepted: 30 April 2024 Published: 10 May 2024
MSC : 34A34, 34C11

In this paper, we investigate the asymptotic stability of the trajectories governed by some delay differential inequalities on time scales. Based on time scale theory and the fixed-point theorem, some sufficient conditions are obtained for guaranteeing asymptotic stability. It is interesting that the inequalities studied in this paper include the generalized Halanay inequalities. Due to the fact that dynamic systems on a time scale unify discrete and continuous systems, the results of this paper have wider application value. Furthermore, some numerical examples verify the main results.
- differential inequalities,
- mixed delays,
- asymptotic stability,
- fixed point theorem,
- time scales
Citation: Bingxian Wang, Mei Xu. Asymptotic behavior of some differential inequalities with mixed delays on time scales and their applications[J]. AIMS Mathematics, 2024, 9(6): 16453-16467. doi: 10.3934/math.2024797

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Abstract

In this paper, we investigate the asymptotic stability of the trajectories governed by some delay differential inequalities on time scales. Based on time scale theory and the fixed-point theorem, some sufficient conditions are obtained for guaranteeing asymptotic stability. It is interesting that the inequalities studied in this paper include the generalized Halanay inequalities. Due to the fact that dynamic systems on a time scale unify discrete and continuous systems, the results of this paper have wider application value. Furthermore, some numerical examples verify the main results.

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