Oscillation Of Solutions And Existence Of Periodic Solutions For Several Class Of Nonlinear Functional Differential Equations

In this paper, we consider oscillatory, asymptotic behavior of solutions and the existence of periodic solutions of the following second and third order nonlinear functional differential equationsSome new sufficient criteria are obtained to characterize oscillatory and asymptotic behavior of solutions of equation (0.1), when o is either the quotient of two odd numbers or one even and one odd numbers. In addition, we establish some existence criteria about periodic solutions of the second and third order equations (0.2) and (0.3) with delays. These results improve and generalize some existing conclusions in the literature. This paper consists of four chapters and is organized as follows:In Chapter 1, we introduce the background and some necessary preliminary knowledge .In Chapter 2, we discuss the oscillatory and asymptotic behavior of solutions of the second order nonlinear differential equation (0.1) and generalize some existing results.In Chapter 3, we study the existence of the periodic solutions of the second order nonlinear differential equation (0.2). By means of Mawhin theorem, we obtain some new sufficient conditions ensuring the existence of the periodic solutions of equation (0.2), and generalize the results obtained in the recent paper [29].In Chapter 4, we consider the existence of periodic solutions of the third order functional differential equation (0.3). By using the recent reference [32] and new analytical technique to estimate the prime bound of J.Mawhin theory, we obtain some sufficient criteria for the existence of periodic solutions, which improve some relative conclusions in the existing references.