Research On The Qualitative Properties Of Solutions Of Several Kinds Of Neutral Differential Equation With Proportional Delays

In this thesis of Master, we investigate a class of second-order neutralpantograph differential equation with positive and negative coefficients and asecond-order nonlinear neutral differential equation with proportional delays. Someoscillation criteria are established. It consists of three chapters.The first chapter gives an introduction on the research background of theproblem and the main work of this paper.In the second chapter, we discuss the oscillation behavior of the solutions of aclass of second-order neutral pantograph differential equation with positive andnegative coefficients of the formSome oscillation criteria are obtained.In the third chapter, we investigate the oscillation of solutions of the followingsecond-order nonlinear neutral differential equation withusing the analysis techniques, we firstly establish the sufficient conditions for theoscillation of all solutions of the homogeneous equation mentioned above. And thenwe study the qualitative properties of solutions of the forced differential equations.