A class of impulsive nonautonomous differential equations and Ulam-Hyers-Rassias stability

Abstract

In this paper, we study a model described by a class of impulsive nonautonomous differential equations. This new impulsive model is more suitable to show dynamics of evolution processes in pharmacotherapy than the classical one. We apply Krasnoselskii's fixed point theorem to obtain existence of solutions. Meanwhile, we mainly present the sufficient conditions on Ulam-Hyers-Rassias stability on both compact and unbounded intervals. Many analysis techniques are used to derive our results.