Oscillations Of Third Order Nonlinear Neutral Differential Equations

The theory of functional differential equations in recent years has attracted the attention of many researchers, in the theory and its applications. The simplest and perhaps most natural type of functional differential equation is a "delay differential equation" .This means an equation expressing some derivative of x at time t in terms of x, the values of the function x at previous times .The importance of the delay differential equations comes from its huge applications for instance ,the study of problems connected with combustion in rocket motion, the problem of planning in economics, biological problems, population dynamics , the logistic equation, and population growth and mechanics, nuclear reactors, heat flow, neural networks, microbiology, ecology, and physiology, as well as many other applications .The study of oscillation and asymptotic properties of solutions of neutral differential equations with positive and negative coefficients has attracted a good bit of attention in the last several years .