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The second order delay differential equation.
Proposition 1.1 means that second order delay equation (1.1) is reduced to nonlinear inequality (1.3) and first order delay differential equation (1.4).
Nonoscillation of second order delay impulsive differential equation was studied in [20].
Sturmian comparison theory for impulsive second order delay equations was studied in [21].
In the first section we describe known results on asymptotic properties of second order delay equations.
In the future, reachable set bounding for second order delay differential equations may be a hot issue, and methods similar to those in this paper may be used to estimate reachable set bounding for second order delay differential equations.
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We consider higher-order delay differential equation.
Consider the third-order delay dynamic equation (3.4).
Example 1 Consider the fifth-order delay differential equation.
Now, we consider the first-order delay dynamic equation (1.9).
For oscillation of the second-order delay dynamic equations, Agarwal et al. [14] considered the second-order delay dynamic equations on time scales.
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