A oscillation theorem for a class of even order neutral differential equations

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Abstract

The even order neutral differential equation dn/dtn[x(t) + h(t)x(t - τ)] + f(t,x(g(t)))=0 is considered under the following conditions: n ≥ 2 is even; τ > 0; h ∈ C(R); g ∈ C [t0,∞), limt→∞ g(t) = ∞; f ∈ C([t0, ∞) × R), uf(t, u) ≥ 0 for (t, u) ∈ [t0, ∞) × R, and f (t, u) is nondecreasing in u ∈ R for each fixed t ≥ t0. It is shown that (1) is oscillatory if and only if the certain non-neutral differential equation is oscillatory, for the case where 0 ≤ μ ≤ h(t) ≤ λ < 1 or 1 < λ ≤ h (t) ≤ μ.

Original languageEnglish
Pages (from-to)172-189
Number of pages18
JournalJournal of Mathematical Analysis and Applications
Volume273
Issue number1
DOIs
Publication statusPublished - 2002 Sep 1
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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