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Zeitschrift für Analysis und ihre Anwendungen


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Volume 16, Issue 2, 1997, pp. 451–462
DOI: 10.4171/ZAA/772

Published online: 1997-06-30

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

Binggen Zhang[1] and Bo Yang[2]

(1) Ocean University of Qingdao, China
(2) Kennesaw State University, United States

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.

Keywords: Oscillation, positive solutions, neutral differential equations

Zhang Binggen, Yang Bo: Equivalence of Oscillation of a Class of Neutral Differential Equations and Ordinary Differential Equations. Z. Anal. Anwend. 16 (1997), 451-462. doi: 10.4171/ZAA/772