On the oscillatory behavior of even order neutral delay dynamic equations on time-scales

Abstract

on an arbitrary time scale T ⊆ R with sup T = ∞ and n ≥ 2 an even integer. Whenever we write t ≥ t1 we mean t ∈ [t1,∞)∩T = [t1,∞)T. We will use the basic concepts and notation for the time scale calculus; we refer the reader to the monograph of Bohner and Peterson [3] for additional details. We shall assume that: (i) α and λ are ratio of positive odd integers; (ii) a, p, and q : T → R = (0,∞) are real-valued rd-continuous functions, a(t) ≥ 0 for t ≥ t0, and