الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
Difference equations appear as natural descriptions of observed evolution, phenomena because most measurements of time evolving variables are discrete and as such those equations are in their own right important mathematical models. More importantly, difference equations also appear in the study of discretization methods for differential equations. Several results in the theory of difference equations have been obtained as more or less natural discrete analogues of corresponding results of differential equations. This is especially true in the case of Lyapunov theory of stability. Nonetheless, the theory of difference equations is a lot richer than the corresponding theory of differential equations. For example ; a, simple difference equation resulting from a first order differential equation may have a phenomena often called appearance of ”ghost” solutions or existence of chaotic orbits that can only happen for higher order differential equations and the theory of difference equations is interesting in itself. The aim of this thesis is to study the qualitative behavior of solution of some nonlinear difference equations of different orders. We discussed, in detail, the following : _ Finding equilibrium points for difference equations. _ Investigating the local stability character of the solutions of difference equations. _ Finding conditions which insure that the solutions of equation are bounded. _ Investigating the global asymptotic stability of the solutions of difference equations. _ Finding conditions which insure that the solutions of equation are periodic with positive prime period two or more. _ Finding conditions for oscillation of solutions. This thesis contains illustrative examples as an application of our results. The thesis consists of six chapters : Chapter (1) is an introductory chapter and it contains some basic definitions, elementary results that will be used throughout the next chapters. In Chapter (2), we study the asymptotic behavior of solutions of class of nonlinear higher order difference equations. In Chapter (3), we study the local stability, periodic, global stability, boundedness of the positive solutions of class of nonlinear difference equations with four variables and positive coefficients. In Chapter (4), we study a more general nonlinear rational difference equations. In Chapter (5), we study the qualitative behavior of solutions of class of nonlinear higher degree difference equations. In Chapter (6), we investigate the boundedness character, the periodicity character, the oscillatory, locally stable and the global stability of the positive solutions of some nonlinear rational difference equations. Our results generalize and complement some of the previous results in the literature (as described in the introduction of chapters). Moreover, some examples are given to illustrate the main results.