This paper devotes to the asymptotic behavior of all solutions of nth order impulsive differential equations. Based on impulsive differential inequality, boundedness and zero tendency of every solution for nth order impulsive differential equations are obtained. In addition, we derive globally uniformly exponential stability of every solution under Lyapunov function and impulsivetechnique, and these results are extend to nth order differential equations with periodic coefficient and periodic impulse. Meanwhile, an example with simulations are provided to verify the conclusion.
| Published in | Science Journal of Applied Mathematics and Statistics (Volume 12, Issue 3) |
| DOI | 10.11648/j.sjams.20241203.12 |
| Page(s) | 43-47 |
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Asymptotic, nth Order, Impulsive Differential Equation
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APA Style
Zheng, Y., Pan, L. (2024). Asymptotic Behavior of nth Order Impulsive Differential Equations. Science Journal of Applied Mathematics and Statistics, 12(3), 43-47. https://doi.org/10.11648/j.sjams.20241203.12
ACS Style
Zheng, Y.; Pan, L. Asymptotic Behavior of nth Order Impulsive Differential Equations. Sci. J. Appl. Math. Stat. 2024, 12(3), 43-47. doi: 10.11648/j.sjams.20241203.12
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Download@article{10.11648/j.sjams.20241203.12,
author = {Yuxin Zheng and Lijun Pan},
title = {Asymptotic Behavior of nth Order Impulsive Differential Equations},
journal = {Science Journal of Applied Mathematics and Statistics},
volume = {12},
number = {3},
pages = {43-47},
doi = {10.11648/j.sjams.20241203.12},
url = {https://doi.org/10.11648/j.sjams.20241203.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20241203.12},
abstract = {This paper devotes to the asymptotic behavior of all solutions of nth order impulsive differential equations. Based on impulsive differential inequality, boundedness and zero tendency of every solution for nth order impulsive differential equations are obtained. In addition, we derive globally uniformly exponential stability of every solution under Lyapunov function and impulsivetechnique, and these results are extend to nth order differential equations with periodic coefficient and periodic impulse. Meanwhile, an example with simulations are provided to verify the conclusion.},
year = {2024}
}
TY - JOUR T1 - Asymptotic Behavior of nth Order Impulsive Differential Equations AU - Yuxin Zheng AU - Lijun Pan Y1 - 2024/06/14 PY - 2024 N1 - https://doi.org/10.11648/j.sjams.20241203.12 DO - 10.11648/j.sjams.20241203.12 T2 - Science Journal of Applied Mathematics and Statistics JF - Science Journal of Applied Mathematics and Statistics JO - Science Journal of Applied Mathematics and Statistics SP - 43 EP - 47 PB - Science Publishing Group SN - 2376-9513 UR - https://doi.org/10.11648/j.sjams.20241203.12 AB - This paper devotes to the asymptotic behavior of all solutions of nth order impulsive differential equations. Based on impulsive differential inequality, boundedness and zero tendency of every solution for nth order impulsive differential equations are obtained. In addition, we derive globally uniformly exponential stability of every solution under Lyapunov function and impulsivetechnique, and these results are extend to nth order differential equations with periodic coefficient and periodic impulse. Meanwhile, an example with simulations are provided to verify the conclusion. VL - 12 IS - 3 ER -
School of Mathematics and Statistics, Lingnan Normal University, Zhanjiang, China
School of Mathematics and Statistics, Lingnan Normal University, Zhanjiang, China
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