Oscillatory And Asymptotic Behavior Of Solutions For Second Order Difference Equations

The dissertation is divided into four sections according to the constent.In Chapter 1, we introduce the background and the main problems of this dissertation.In Chapter 2, we study the oscillation and asymptotic behavior for second order nonlinear differential equation whereσis a quotient of two odd positive integers. By using the Riccati transfor-mation and three sets of functions, we obtain several new results, which extend and improve some existing results.In Chapter 3, we study the oscillation for second order nonlinear differential equation with perturbation where a is a quotient of two odd positive integers. By classifying the regular solutions of this equation and using generalized Riccati transformation, we obtain several new results, which extend and improve some existing results.In Chapter 4, we study the oscillation and asymptotic behavior for second order nonlinear differential equation with perturbation whereσis a quotient of even integer over odd integer. By classifying the regular solutions of this equation and using generalized Riccati transformation, we obtain several new results, which extend and improve the known results.Examples are also given to illustrate our results in the last three chapters, respectively.