Oscillation for higher order superlinear delay differential equations with unstable type

We first show that the n-order superlinear delay differential equation with unstable type x(n)(t )= p(t) x(t − τ) α−1 x(t − τ), t t0, always has an unbounded and nonoscillatory solution, wheren>1 is an even integer, p ∈ C([t0,∞), [0,∞)), τ >0 and α > 1. Then an almost sharp bounded oscillation and nonoscillation criterion is obtained.  2003 Elsevier Inc. All rights reserved.