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Existence and Uniqueness Results for Quaternion-Valued Nonlinear Impulsive Differential Systems

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Abstract

This paper studies the existence and uniqueness conditions for the quaternion-valued nonlinear impulsive system. Firstly, a space of quaternion-valued piecewise functions is constructed and completeness of the space is also proved. Then by taking advantage of the Bielecki norm and fixed point theorem, existence and uniqueness criteria of quaternion-valued nonlinear impulsive system are obtained. At last, an example is given to illustrate our theoretical results.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Tongji University, Shanghai, 200092, China

    Jingwen Zhu & Jitao Sun

  2. College of Mathematics and Physics, Jinggangshan University, Jinggangshan, 343009, China

    Jingwen Zhu

  3. Institute for Intelligent Systems, University of Johannesburg, Johannesburg, South Africa

    Jitao Sun

Authors
  1. Jingwen Zhu
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  2. Jitao Sun
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Correspondence to Jingwen Zhu.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 61673296.

This paper was recommended for publication by Editor LIU Yungang.

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Zhu, J., Sun, J. Existence and Uniqueness Results for Quaternion-Valued Nonlinear Impulsive Differential Systems. J Syst Sci Complex 31, 596–607 (2018). https://doi.org/10.1007/s11424-017-6158-9

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  • DOI: https://doi.org/10.1007/s11424-017-6158-9

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