OSCILLATION OF THIRD-ORDER NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS WITH DISTRIBUTED TIME DELAY - Xiang, Haifei (Italian Journal of Pure and Applied Mathematics, 2016)
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.