The Stability Of A Class Of Retarded Functional Differential Equations And Related Issues

The theory of stability is a basic and important subject in the theories of differential equations. By constructing suitable Lyapunov functionals, we explore the uniformly asymptotic stability of a class of retarded functional differential equations with finite and infinite delays, via Lyapunov second method, especially the delays here vary with time. Moreover, we study the existence, the uniqueness and the stability of periodic solutions and almost periodic solutions of the corresponding systems with periodic perturbations arid almost periodic perturbations. More general and applicable results are derived, which improve and generalize the main results in [23.24].The tree of this paper is as follows: in chapter 2, we study the uniformly asymptotic stability of the trivial solutions of a class of linear and nonlinear difference-differential equations with finite time-dependent delays. Then, we deal with the existence, the uniqueness and the stability of periodic solutions and almost periodic solutions when the systems are under periodic perturbations and almost periodic perturbations. In chapter 3, we devote ourselves to investigating the similar problems for a class of linear and nonlinear integro-differential equations with infinite and time-dependent delays. We use the theories of the phase space G'/i, which were introduced by Qichang Huang and Ke Wang[19,20,21,22], to overcome the difficulty caused by infinite delays. With the help of the more general and effective Lyapunov functionals, we derive new criteria for the uniformly asymptotic stability.