الفهرس 
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Abstract
In this thesis we study the qualitative behavior of solutions of some nonlinear difference equations of different orders. Recently, difference equations have started to receive much attention from scientists and from various disciplines. This thesis breaks into a preface, four chapters, and a list of references.
Chapter 1 is an introduction where we present a brief survey of the history of computing with recurrences.
In chapter 2 we study the oscillation of the solution to second order nonlinear difference equations with damping term of the form
where for any sequence of real numbers, is the ratio of odd positive integers, and are sequences of real numbers. Examples illustrating the importance of our results are also given.
In Chapter 3 we study the behavior of solutions of the higher order rational difference equation
where the initial conditions are arbitrary positive real numbers, is nonnegative integer and are positive constants.
Also, we study the behavior of solutions of the higher order rational difference equation
where the initial conditions are arbitrary positive real numbers, is nonnegative integer and are positive constants.
In Chapter 4 we investigate the solutions, stability character and asymptotic behavior of the first order system of difference equations
where and initial conditions
Moreover, in this chapter we deal with periodicity of solutions for three dimensional system of higher order difference equations
with a nonzero real numbers initial conditions. Some numerical simulations to this system are given to illustrate our results.