Oscillations Of Two Kinds Of Difference Equations

This paper consists of four chapters , which mainly investigated the oscillatory behavior of second order half-linear difference equations and higher order nonlinear difference equations with continuous variables.In chapter 1, we introduce the historical background of problems which will be investigated and state the main results of the thesis. In addition, we list some preliminary knowledge which is needed in the thesis.In chapter 2, we study the oscillatory behavior of half-linear difference equations. By using Riccati transformation, Abel transformation and Lagrange mean value theorem, we established some oscillation criteria for this kind of equation. Our results are the discrete form of the main results in [21].Chapter 3 is concerned with the oscillatory behavior of the even order nonliear difference equations with continuous variables. By using the iterated integral transformations and some new techniques, we obtained some oscillation criteria. A example which dwells upon the importance of our results is also included.Finally, we present an outline of the article and some prospects in the field.