The problem of a lazy tester, or exponential dichotomy for impulsive differential equations revisited

摘要

For the impulsive equation in a Banach spaceX'(t)+a(t)x(t)=o,t>0,x(t_j~-)+a_j,we study the type of stability which can be deduced if a solution is bounded for any bounded sequence {αj}. Under certain restrictions on the distance between impulses we can obtain either exponential or asymptotic stability, with a guaranteed polynomial degree (as t?r) of solution decay. A similar scheme is applied to equations with piecewise constant arguments and to integrodifferential equations.