JournalszaaVol. 16, No. 2pp. 451–462

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

  • Binggen Zhang

    Ocean University of Qingdao, China
  • Bo Yang

    Kennesaw State University, United States
Equivalence of Oscillation of a Class of Neutral Differential Equations and Ordinary Differential Equations cover
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Abstract

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

(x(t)x(tr))(n)+p(t)x(tσ)=0   and   x(n+1)(t)+p(t)rx(t)=0(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)0p(t) ≥ 0 and n1n ≥ 1 is odd, from which we obtain some new oscillation conditions and comparison theorems for the first of these equations.

Cite this article

Binggen Zhang, Bo Yang, Equivalence of Oscillation of a Class of Neutral Differential Equations and Ordinary Differential Equations. Z. Anal. Anwend. 16 (1997), no. 2, pp. 451–462

DOI 10.4171/ZAA/772