TY - JOUR

T1 - A necessary and sufficient condition for the oscillation in a class of even order neutral differential equations

AU - Tanaka, Satoshi

PY - 2000

Y1 - 2000

N2 - The even order neutral differential equation (1.1) (equation presented) is considered under the following conditions: n ≥ 2 is even; λ > 0; T > 0; 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 equation (1.1) is oscillatory if and only if the non-neutral differential equation (equation presented) is oscillatory.

AB - The even order neutral differential equation (1.1) (equation presented) is considered under the following conditions: n ≥ 2 is even; λ > 0; T > 0; 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 equation (1.1) is oscillatory if and only if the non-neutral differential equation (equation presented) is oscillatory.

KW - Neutral differential equation

KW - Oscillation

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U2 - 10.14232/ejqtde.2000.1.4

DO - 10.14232/ejqtde.2000.1.4

M3 - Article

AN - SCOPUS:0011379673

SN - 1417-3875

SP - 1

EP - 27

JO - Electronic Journal of Qualitative Theory of Differential Equations

JF - Electronic Journal of Qualitative Theory of Differential Equations

ER -