Stability Switches Of Retarded Differential Difference Systems And Existence Of Positive Periodic Solutions Of Neutral Functional Differential Equations

This paper is divided into two parts. The first part is concerned with the stability switches for two classes of retarded differential difference systems, while the second part discusses the existence of positive periodic solutions of neutral functional differential equations.The study on the stability switches of functional differential difference equations is an important research branch of the stability theories, which of both the theory and its applications has broad prospects.The first part of this paper, chapter 2 and 3, deals with the stability switches for two classes of retarded differential difference systems, respectively. By analyzing the characteristic roots of characteristic equations, some algebraic criteria of stability switches are established, which are useful and easy to verify. An example is given to illustrate the results with by resorting to computer simulations.Recently, the monotone semiflow theory of functional differential equations has gotten great development, which has the strong attention to authors all over the world. The second part, chapter 4, is devoted to the existence of positive periodic solutions for neutral functional differential equations by appealing to monotone semiflow theories. By combining the theory of monotone semiflows generated by neutral functional differential equations and Schauder's fixed point theorem, some sufficient conditions are derived and an example is given to illustrate the results.