Boundedness and periodicity in impulsive ordinary and functional differential equations

Abstract

In this paper, we study the boundedness and periodicity of solutions for impulsive ordinary differential equations (ODEs) and functional differential equations (FDEs). By using Horn’s fixed point theorem, Hale–Yoshizawa type criteria for the existence of T -periodic solutions are established. To use these criteria, we also give two new boundedness theorems, and establish new existence results for T -periodic solutions which show that the impulsive perturbations do contribute to yielding periodic solutions even when the underlying systems do not enjoy periodic solutions.