Some Results In The Research Of The Differential Equations

In this dissertation, the existences of periodic solutions, almost periodic solutions and pseudo almost periodic solutions for several classes of functional differential equations are investigated. This dissertation is organized by four parts: In Chapter 1, we simply introduce the development of differential equations with piecewise constant argument and periodic solutions for a class of general utility type nerve network model. In Chapter 2, we consider a class of generalized second-order neutral delay differential equations with piecewise constant argument; by constructing almost periodic solutions of the difference equation and using the fixed point theorem, we obtain a sufficient condition of the existences of almost periodic solutions of the equation. In Chapter 3, we generalize the sufficient condition of the existences of pseudo almost periodic solutions of second-order neutral delay differential equations with piecewise constant argument in reference [12]. In Chapter 4, we consider a class of generalized general utility type nerve network model with delay; by using the matrix measure and the fixed point theorem, we obtain a new sufficient condition of the existences of periodic solutions of the model.