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Razumikhin method for impulsive functional differential equations of neutral type

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  • Li, Xiaodi
  • Deng, Feiqi

Abstract

Although the well-known Razumikhin method has been well developed for the stability of functional differential equations with or without impulses and it is very useful in applications, so far there is almost no result of Razumikhin type on stability of impulsive functional differential equations of neutral type. The purpose of this paper is to close this gap and establish some Razumikhin-based stability results for impulsive functional differential equations of neutral type. A kind of auxiliary function N(t) that has great randomicity is introduced to Razumikhin condition. Some examples are given to show the effectiveness and advantages of the developed method.

Suggested Citation

  • Li, Xiaodi & Deng, Feiqi, 2017. "Razumikhin method for impulsive functional differential equations of neutral type," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 41-49.
    • Handle: RePEc:eee:chsofr:v:101:y:2017:i:c:p:41-49
    DOI: 10.1016/j.chaos.2017.05.018
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    References listed on IDEAS

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    1. Jiang, Fangfang & Sun, Jitao, 2016. "On the existence of discontinuous periodic solutions for a class of Liénard systems with impulses," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 259-265.
    2. Park, Ju H. & Kwon, O.M., 2008. "Stability analysis of certain nonlinear differential equation," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 450-453.
    3. Zeng, Xu & Li, Chuandong & Huang, Tingwen & He, Xing, 2015. "Stability analysis of complex-valued impulsive systems with time delay," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 75-82.
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    Citations

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    Cited by:

    1. Ruofeng Rao & Shouming Zhong, 2017. "Stability Analysis of Impulsive Stochastic Reaction-Diffusion Cellular Neural Network with Distributed Delay via Fixed Point Theory," Complexity, Hindawi, vol. 2017, pages 1-9, September.
    2. Gui-Lai Zhang & Yang Sun & Ya-Xin Zhang & Chao Liu, 2024. "Euler Method for a Class of Linear Impulsive Neutral Differential Equations," Mathematics, MDPI, vol. 12(18), pages 1-19, September.
    3. Yunfeng Li & Pei Cheng & Zheng Wu, 2022. "Exponential Stability of Impulsive Neutral Stochastic Functional Differential Equations," Mathematics, MDPI, vol. 10(21), pages 1-17, November.
    4. Yang Sun & Gui-Lai Zhang & Zhi-Wei Wang & Tao Liu, 2023. "Convergence of the Euler Method for Impulsive Neutral Delay Differential Equations," Mathematics, MDPI, vol. 11(22), pages 1-14, November.
    5. Wang, Pengfei & Zou, Wenqing & Su, Huan, 2019. "Stability of complex-valued impulsive stochastic functional differential equations on networks with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 338-354.

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