In this thesis we investigate the oscillation and nonoscillation behavior of solutions of nonlinear difference equations. A solution of a difference equation is called nonoscillatory if it is eventually positive or negative; otherwise it is said to be oscillatory. We will state and prove several oscillation criteria for solutions of second and higher order nonlinear difference equations. In chapter 2, we first give some known oscillation criteria for solutions of higher order neutral type difference equations, and then derive several new results for the same equation. Sufficient conditions are also established for the existence of positive solutions. Chapter 3 deals with oscillation of solutions of second order nonlinear difference equations with damping. New oscillation criteria are established by using the averaging method.
 
 

Keywords: Oscillation, Difference equation, Neutral equation, Positive solution, Averaging method.