Oscillation Behavior for a Class of Second Order Neutral Differential Equation

Abstract

Due to the extensive application of differential equation, the study of its vibration has been paid much attention. In this paper, we research the oscillation behavior of a class of second order dynamic models. This research is suit to the fields of engineering technique, aviation technology, automation control and so on. We analyse a class of second order neutral differential equation. First, we give a neutral dynamic model and analysis the research status of model. After that, we research its oscillation behavior and found a some of new sufficient conditions of the oscillatory property, a number of new Oscillation criteria for both andare founded for equation by making use of the generalized Riccati transformation and specific analytical skills. Our results are new and these results enrich and refine existing results. The results are verified by numerical experiments. Because of the neutral dynamic system model has an important status and action in engineering technique, aviation technology, automation control. As a result, our research is of big help to engineering technology, aviation technology, and automation control.