Oscillation And Asymptotic Behavior Of Functional Differential Equation And Difference Equation

This Master thesis is composed of seven sectors .Mainly,we study the oscillation, asymptotic behaviour, stability of Functional Differential Equations with delay and Difference Equations.In the first chapter, we introduce some relating definitions,symbols and theorems .In the second chapter ,the oscillation of neutral difference equations with continuous arguments is discussed in this paper some sufficient conditions for the oscillation of solutions of the equation are obtained , improve and extend some result of[4].In the third chapter, we mainly deals with the oscillation and stability of the delaydifference equation , where the coefficient is periodic.And we get some new results by the lineared method.In the fourth chapter, we mainly discusses nonoscillatory solutions classification of second order nonlinear difference equations.And also gives some necessary and sufficient conditions to the solutions existence .In the fifth chapter, we mainly discuss the equationand obtain some necessary and sufficient conditions about the solutions of (5.0) tend to 0 or ±∞ as t →∞ or oscillatory. And partily improve the works of [33].