Journal of Systems Science and Complexity

, Volume 31, Issue 3, pp 596–607 | Cite as

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.

Keywords

Differential equations existence and uniqueness impulsive system quaternion-valued 

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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of MathematicsTongji UniversityShanghaiChina
  2. 2.College of Mathematics and PhysicsJinggangshan UniversityJinggangshanChina
  3. 3.Institute for Intelligent SystemsUniversity of JohannesburgJohannesburgSouth Africa

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