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Stability criteria of nonlinear impulsive differential equations with infinite delays

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Abstract

In this paper, we consider the uniform stability and uniformly asymptotical stability of nonlinear impulsive infinite delay differential equations. Instead of putting all components of the state variable x in one Lyapunov function, several Lyapunov-Razumikhin functions of partial components of the state variable x are used so that the conditions ensuring that stability are simpler and less restrictive; moreover, examples are discussed to illustrate the advantage of the results obtained.

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Authors and Affiliations

  1. Department of Mathematics, Southeast University, Nanjing, 210096, China

    Yang Liu

  2. College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, 321004, China

    Yang Liu & Xiu-shan Cai

  3. Graduate School, Zhejiang Normal University, 321004, Jinhua, China

    Bo Wu

Authors
  1. Yang Liu
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  2. Bo Wu
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  3. Xiu-shan Cai
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Corresponding author

Correspondence to Yang Liu.

Additional information

Supported by the National Natural Science Foundation of China (Nos. 11101373, 61374077 and 11271333) and the Natural Science Foundation of Zhejiang Province of China (No. LY14A010008).

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Liu, Y., Wu, B. & Cai, Xs. Stability criteria of nonlinear impulsive differential equations with infinite delays. Acta Math. Appl. Sin. Engl. Ser. 31, 921–934 (2015). https://doi.org/10.1007/s10255-015-0495-z

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  • DOI: https://doi.org/10.1007/s10255-015-0495-z

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