An analysis for a special class of solution of a Duffing system with variable delays

Ramazan Yazgan; Ramazan Yazgan

doi:10.3934/math.2021649

AIMS Mathematics

2021, Volume 6, Issue 10: 11187-11199. doi: 10.3934/math.2021649

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Research article

An analysis for a special class of solution of a Duffing system with variable delays

Ramazan Yazgan ^,

Faculty of Science, Department of Mathematics, Van Yüzüncü Yil University, Van, Turkey

Received: 16 March 2021 Accepted: 01 July 2021 Published: 03 August 2021
MSC : 34K14, 34K40

In this study, we are concerned the existence of pseudo almost automorphic (PAA) solutions and globally exponential stability of a Duffing equation system with variable delays. Some differential inequalities and the well-known Banach fixed point theorem are used for the existence and uniqueness of PAA solutions. Also, with the help of Lyapunov functions, sufficient conditions are obtained for globally exponential stability of PAA solutions. Since the PAA is more general than the almost and pseudo almost periodicity, this work is new and complementary compared to previous studies. In addition, an example is given to show the correctness of our results.
- Lyapunov function,
- Pseudo almost automorphic,
- Banach fixed point theorem,
- exponential stability,
- Duffing equation system
Citation: Ramazan Yazgan. An analysis for a special class of solution of a Duffing system with variable delays[J]. AIMS Mathematics, 2021, 6(10): 11187-11199. doi: 10.3934/math.2021649

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Abstract

In this study, we are concerned the existence of pseudo almost automorphic (PAA) solutions and globally exponential stability of a Duffing equation system with variable delays. Some differential inequalities and the well-known Banach fixed point theorem are used for the existence and uniqueness of PAA solutions. Also, with the help of Lyapunov functions, sufficient conditions are obtained for globally exponential stability of PAA solutions. Since the PAA is more general than the almost and pseudo almost periodicity, this work is new and complementary compared to previous studies. In addition, an example is given to show the correctness of our results.

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