Some New Results on Robustness for Impulsive Differential Equations

In this paper, we investigate the robustness of impulsive differential equations in Banach spaces. We establish sufficient conditions to ensure that nonuniform exponential contractions, nonuniform exponential expansions and nonuniform exponential dichotomies of impulsive differential equations persist within a wider range of perturbations. It is worth emphasizing that the new results provide some significant improvements of existing results in the case where the perturbations are not required to be sufficiently small. Moreover, the conditions of our conclusions even for differential equations without impulse are more relaxed. Finally, we illustrate our results with a concrete example.