Research On Oscillation Of Several Classes Of Neutral Functional Differential Equations

This thesis is composed of four chapters. In this article, we mainly discuss the oscillation of several classes of neutral functional differential equations, and obtain some new results for the oscillation of all of their solutions by making use of generalized Riccati transformation, introducing parameter function and using integral averaging technique. Our results presented in this paper extend and improve some known results in the literature.In chapter 1, we introduce the background of the problem and the recent development of the research in this field.In chapter 2, we study the oscillation behavior of solutions of certain first order neutral functional differential equations with distributed delay. Some general sufficient conditions for the oscillation of solutions of the equations are established. The results obtained in this chapter improve some known results in the literature.In chapter 3, we discuss the oscillation of all solutions of some second order neutral nonlinear functional differential equations with damping term. Three oscillatory criteria are obtained, and some known results in the literature are extended.In the last chapter, we consider the oscillation behavior of solutions of a class of even-order neutral functional differential equations with distributed delay and damping term. Three oscillatory theorems are presented, and some known results in the literature are generalized.