Globally Exponential Stability of Piecewise Pseudo Almost Periodic Solutions for Neutral Differential Equations with Impulses and Delays

In this paper, a kind of delayed impulsive neutral differential equations (DINDEs) has been studied. By making the use of contraction mapping principle and generalized Gronwall-Bellmain inequality, some novel and sufficient conditions on the existence and uniqueness of the piecewise pseudo almost periodic (PAP) solutions are established. Furthermore, by applying the definition of the globally exponential stability and inequality technology, the globally exponential stability of the piecewise PAP solutions of the addressed DINDE is obtained. The established results of this paper are new and some previous related works are extended and included. Finally, one numerical example is exploited to illustrate the advantages of the established theoretical results.

Automated summary

This paper studies a kind of delayed impulsive neutral differential equations (DINDEs) and establishes conditions for the existence, uniqueness, and global exponential stability of the solutions using contraction mapping principle and inequality technology.