Delay Differential Equations Of Pseudo Almost Periodic Solutions And Stability

It seems that the strong interest in the differential equations with piecewise constant argument is motivated by the fact that they describe hybrid dynamical systems which is a combination of the properties of both differential and difference equations. There have been many pa-pers(such as[7] ~ [15])concerning these equations. At first, most papers concerned the stability ,the existence of periodic solutions and the oscillation(such as [16] ~ [19]). Recently the existence of almost periodic solutions of this type of equations are also considered in some papers(such as [16] ~ [19]).In [20],Zhang chuanyi has introduced an extension of the almost periodic functions,the so-called pseudo-almost periodic functions . Then, the existence of pseudo-almost periodic solutions of some differential equations with piecewise constant argument is considered in some papers([21] ~ [25]). The main purpose of the first chapter in this paper is to investigate the existence of pseudo-almost periodic solutions of a kind of differential equations with piecewise constant argument of which the almost periodic solutions have been considered .The asymptotic stability of some nonlinear second-order difference equations is considered in the second chapter.We present some general results of the equations . Nevertheless, the asymptotic stability of these kind of equations is a fertile area for research.In the third chapter we have given some sufficient conditions ,which extend the conclusion before ,to guarantee the stability of a kind of neutral functional differential equations.