Oscillation Behavior Of Solutions Of Higher Order Nonlinear Neutral Differential Equations

This paper , consisting of three chapters , intends to describe the oscillation behavior of two classes of delay differential equations.Chapter 1 is a brief introduction to the historical background and the significance of this study and outlines the recent development for the oscillation of delay differential equations.Chapter 2 is a study on the even order superlinear delay differential equation with unstable type. By constructing a solution of the inequality corresponding the equation and by using Banach contraction principle, I prove that the equation always has an unbounded and eventually solution. Then I establish an necessary and sufficient conditions for oscillation of higher order nonlinear neutral delay differential equations.Chapter 3 is a study on existence of positive solutions of the odd order nonlinear delay differential equation. By using Lebesgue convergence control theorem and Banach contraction principle to prove existence of positive solutions.