Nonautonomous impulsive differential equations of alternately advanced and retarded type

Abstract

A variation of parameters formula and Gronwall type integral inequality are proved for a impulsive differential equation involving piecewise alternately advanced and retarded argument. At the same time, we study its oscillation and asymptotic stability properties.
Our results are new, extend and improve earlier publications. Several numerical examples and simulations are also given to show the feasibility of our results.