Stability analysis for $ (\omega, c) $-periodic non-instantaneous impulsive differential equations

Kui Liu; Kui Liu

doi:10.3934/math.2022101

AIMS Mathematics

2022, Volume 7, Issue 2: 1758-1774. doi: 10.3934/math.2022101

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Research article

Stability analysis for $ (\omega, c) $-periodic non-instantaneous impulsive differential equations

Kui Liu ^,

College of Science, Guizhou Institute of Technology, Guiyang, Guizhou 550025, China

Received: 03 September 2021 Accepted: 22 October 2021 Published: 02 November 2021
MSC : 34A08, 34A37, 34C25

In this paper, the stability of $ (\omega, c) $-periodic solutions of non-instantaneous impulses differential equations is studied. The exponential stability of homogeneous linear non-instantaneous impulsive problems is studied by using Cauchy matrix, and some sufficient conditions for exponential stability are obtained. Further, by using Gronwall inequality, sufficient conditions for exponential stability of $ (\omega, c) $-periodic solutions of nonlinear noninstantaneous impulsive problems are established. Finally, some examples are given to illustrate the correctness of the conclusion.
- non-instantaneous impulsive differential equations,
- $ (\omega, c) $-periodic solutions,
- stability
Citation: Kui Liu. Stability analysis for $ (\omega, c) $-periodic non-instantaneous impulsive differential equations[J]. AIMS Mathematics, 2022, 7(2): 1758-1774. doi: 10.3934/math.2022101

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Abstract

In this paper, the stability of $ (\omega, c) $-periodic solutions of non-instantaneous impulses differential equations is studied. The exponential stability of homogeneous linear non-instantaneous impulsive problems is studied by using Cauchy matrix, and some sufficient conditions for exponential stability are obtained. Further, by using Gronwall inequality, sufficient conditions for exponential stability of $ (\omega, c) $-periodic solutions of nonlinear noninstantaneous impulsive problems are established. Finally, some examples are given to illustrate the correctness of the conclusion.

References

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