On Oscillation For Several Classes Nonlinear Higher-order Differential Equations

The oscillation theory of differential equations is an important branch of the theory of differential equations. It has deep physical background and mathemat-ical models. In this dissertation, we employ a generalized Riccati transformation, the estimations of inequalities, integral average technique and monotonicity of a function to investigate the oscillation problems for several classes of higher-order nonlinear differential equations. We obtain some meaningfully new results.This dissertation is divided into four sections according to the content.In Chapter 1, we introduce the background and the main problems of this dissertation.In Chapter 2, we obtain new oscillation critera of the higher-order nonlinear differential equation by employing functions H(t,s) and h(t,s), integral average technique and the estimations of inequalities. An example illustrating the sharpness of our results is also provided.In Chapter 3, new oscillation criteria for higher-order diffferential equation where a> 0, Z(t) = x(t)+p(t)x(τ(t)), are established under the conditions or by employing generalized Riccati transformation and integral average technique. The obtained results extend and improve the ones in Ye and Xu. An example illustrating the application of our results is also provided. In Chapter 4, we study the oscillation of the higher-order nonlinear differen-tial equation By employing generalized Riccati transformation and integral average technique, we obtain new oscillation criteria, which extend and improve the known results. At the end of this chapter, we give several oscillation criteria in the subinterval of [t0,∞).