Growth in an impulsive integral inequality

摘要

In this paper we study a finite-sum integral inequality with a sequence of impulses. Making a sequential monotonization, we give recursively defined functions to estimate solutions of the inequality piecewise. In order to use the estimate to study boundedness and asymptotics of solutions for differential equations, we regard the estimating function as a solution of a nonautonomous difference equation, simplify the equation with composition of operators, and reduce our discussion to qualitative analysis of the difference equation so that we give results on monotonicity, boundedness and α-weighted boundedness for solutions of the inequality. As applications, we study boundedness and asymptotics of solutions for two impulsive differential equations.