Abstract:

This paper studies the oscillation and asymptotic properties of delay differential equations with damping and sub-linear neutral terms using the generalized Riccati transformation technique and the mean value theorem. After analyzing the function of the cross-link between the condition $\int^\infty_{t_0}(\frac{1}{R(t)})^{\frac{1}{\gamma}}{\rm{d}}t=\infty$ and the relationship of parameters $\gamma$ and $\beta$ in the differential equations oscillation, the sufficient conditions for the existence of vibration solutions are provided to extend the existing results in the cited literature. Lastly, some applications are given to illustrate the significance of these results.

Key words: damping, delay, sub-linear neutral terms, differential equations, oscillation