In this paper; we establish the equivalence of the oscillation of the two equations

$$
(x(t) - x(t - r))^{(n)} + p(t) x(t - \sigma) = 0 \ \ \ \mathrm {and} \ \ \ x^{(n+1)}(t) + \frac{p(t)}{r} x(t) = 0
$$

where $p(t) ≥ 0$ and $n ≥ 1$ is odd, from which we obtain some new oscillation conditions and comparison theorems for the first of these equations.

Equivalence of Oscillation of a Class of Neutral Differential Equations and Ordinary Differential Equations

Binggen Zhang

Bo Yang

Abstract

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