| 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. |
