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.
|Number of pages||18|
|Journal||Journal of Mathematical Analysis and Applications|
|Publication status||Published - 2002 Sept 1|
ASJC Scopus subject areas
- Applied Mathematics