الفهرس 
IntroductionOnly 14 pages are availabe for public view
 |  | from | 116 |  |  |
| | | from | 116 | | |
Abstract
In this thesis we study the oscillation and asymptotic behavior of all solutions of nonlinear second order difference equations. The study of difference equations has had important growth in the last years, not only as a fundamental tool in the discretization of a differential equation, but also as a useful model for several economical and population problems. Our main objective in this work is to study the oscillation behavior of solutions for both homogeneous or nonhomogeneous second order nonlinear difference equations. Also, we will discuss the oscillation of the solutions of second order nonlinear difference equation with damping term. This thesis breaks into a preface, five 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 oscillatory behavior of the second order nonlinear homogeneous difference equations. Using Riccati transformation, we derive some oscillation criteria of the above homogenous difference equations. Our results improve and generalize some recent oscillation criteria. Examples illustrating the importance of our results are also given. Chapter 3 deals with the oscillation of all solutions for the second order nonlinear nonhomogeneous difference equations. Two cases will be investigated separately, the superlinear and the sublinear one. Necessary and sufficient conditions for oscillation of all solution are obtained for both superlinear and sublinear cases. Chapter 4 is devoted to study the oscillation of solutions of the second order nonlinear difference equations with a damping term. New oscillation criteria for second order superlinear damped difference equation are obtained. In Chapter 5 we establish the asymptotic behavior of the second order nonlinear nonhomogeneous difference equations. Our purpose is to provide sufficient conditions, which ensure that every oscillatory solutions to be bounded or to converge to zero.