ABSTRACT
This chapter introduces the linearized oscillation results for a certain class of second order nonlinear delay differential equations. It presents results on the existence of oscillatory solutions of the delay differential equation. The chapter also presents Sturm comparison theorems which are very useful for the oscillation theory as well as the boundary value problems. It establishes some oscillation criteria for second order neutral differential equations. By way of these criteria the oscillation problem for neutral differential equations can be reduced to the same problem for the corresponding delay equations and sometimes to the corresponding ordinary differential equation. The chapter describes the classification of nonoscillatory solutions for second order nonlinear neutral differential equations and various existence results of nonoscillatory solutions of different types. It deals with the forced oscillation. The chapter investigates equations with nonlinear neutral terms. It establishes a relation between the oscillation of equation of the advanced type and the oscillation of the corresponding ordinary differential equation.
