Ulam-Type Stability Analysis For A Class Of Non-Instantaneous Impulsive Differential Systems

In this paper,existence of solutions and Ulam-type stability for a class of non-instantaneous impulsive differential systems are investigated by two different methods.By means of Krasnoselskii's fixed point theorem,existence of solutions of the related system is proven.By analyzing the relationship between the solutions of the original system and the disturbed system,some sufficient conditions are established to conclude Ulam-type stability of the studied system.The monotone iterative sequences of upper and lower solutions are constructed and the minimal and maximal solutions of the system are obtained.Based on the upper and lower solution method,in the case n(28)1,certain sufficient conditions are given to guarantee Ulam-type stability of the corresponding scalar equations.Finally,two examples are provided to illustrate the effectiveness of the obtained results.