Abstract
Based on Riccati transformation and the inequality technique, we establish some new sufficient conditions for oscillation of the second-order neutral delay dynamic equations on time scales. Our results not only extend and improve some known theorems, but also unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation on time scales. At the end of this paper, we give an example to illustrate the main results.
Highlights
The theory of time scales was first proposed by Hilger [1] in order to unify continuous and discrete analysis
In this paper we study and give the sufficient conditions for oscillation of the second-order neutral delay dynamic equation
It is well known by reserchers in this field that an dynamic equation is called oscillatory in case all its solutions are oscillatory, and a solution of the equation is said to be oscillatory if it is neither eventually positive nor eventually negative
Summary
The theory of time scales was first proposed by Hilger [1] in order to unify continuous and discrete analysis. (2016) On the Oscillation of Second-Order Nonlinear Neutral Delay Dynamic Equations on Time Scales. It is well known by reserchers in this field that an dynamic equation is called oscillatory in case all its solutions are oscillatory, and a solution of the equation is said to be oscillatory if it is neither eventually positive nor eventually negative. We only discuss those solutions x of Equation (1.1) that are not eventually zero in this paper.
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