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

This paper studies the existence and uniqueness conditions for the quaternion-valued non-linear 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.