New oscillation theorems for a class of even-order neutral delay differential equations

Abstract

In this work, we study the oscillatory behavior of even-order neutral delay differential equations $\upsilon ^{n}(l)+b(l)u(\eta (l))=0$ υ n ( l ) + b ( l ) u ( η ( l ) ) = 0 , where $l\geq l_{0}$ l ≥ l 0 , $n\geq 4$ n ≥ 4 is an even integer and $\upsilon =u+a ( u\circ \mu ) $ υ = u + a ( u ∘ μ ) . By deducing a new iterative relationship between the solution and the corresponding function, new oscillation criteria are established that improve those reported in (T. Li, Yu.V. Rogovchenko in Appl. Math. Lett. 61:35–41, 2016).

Conditions for the Oscillation of Solutions to Neutral Differential Equations of Higher Order

“…where ϕ(s) = |s| p−2 s and the obtained properties for the oscillation of (4). Anis and Moaaz [15] investigated the oscillatory behavior of even-order neutral differential equations of the form…”