OSCILLATION OF THIRD-ORDER NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS WITH DISTRIBUTED TIME DELAY

Abstract

With the development of modern society, research on properties of ordinary differential equation is becoming one of the hotspots in mathematical field.  Neutral differential equation which is usually generated in natural science and engineering field is always extensively concerned by many scientific researchers for it can effectively describe multiple complex phenomena in natural world.  
In recent years, differential equation and non-linear differential equation with time delay have attracted more and more attention.  However, few researches concern about the properties of neutral differential equations with time delay.  On account of this, we explored the oscillation of third-order nonlinear neural delay differential equations.  Based on operators and integration techniques and with the help of proper comparison theorem, we established some oscillation sufficient conditions for several new solutions to such kind of equation.  The obtained theorem which popularizes and improves results of the existing literature is applicable to neural differential equations.  These results fully reflect the effects of time delay in oscillation of equation.