الفهرس | Only 14 pages are availabe for public view |
Abstract The main objective of this thesis is to shed light on many equations of fourth and higher order, through studying the oscillation of solutions of those equations by different methods and comparison of results. We discussed, in detail, the oscillation of fourth and higher-order nonlinear delay differential equations.For the sake of convenience and clarity, we will use some main techniques for finding the oscillation criteria, including the following:Riccatti transformation technique.New comparison principles .Integral averaging technique.This thesis contains several remarks and illustrative examples as an application of our results. The thesis consists of four chapters:Chapter 1. This chapter is an introductory chapter and it deals with the problem of oscillation of fourth/higher-order functional differential equations. It contains some basic definitions, elementary results that will be used throughout the next chapters.Chapter 2. In this chapter, we study the oscillation of a fourth order delay differential equation with deviating arguments by using comparison theorem and riccatti transformation technique. Also, on the other hand, this chapter deals with the oscillation and behavior of solutions of fourth order advanced differential equation.Chapter 3. By using integral averaging method we are concerned with the oscillation of the fourth order neutral delay differential equations with delayed argument.Chapter 4. During this Chapter, we are studied with the oscillation of solutions of higher order nonlinear differential equations, we used Comparison method to prove our results. |