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

Abstract

Abstract In this work, we study the oscillatory behavior of even-order neutral delay differential equations υ n ( l ) + b ( l ) u ( η ( l ) ) = 0 $\upsilon ^{n}(l)+b(l)u(\eta (l))=0$ , where l ≥ l 0 $l\geq l_{0}$ , n ≥ 4 $n\geq 4$ is an even integer and υ = u + a ( u ∘ μ ) $\upsilon =u+a ( u\circ \mu ) $ . 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).

Keywords

• Even-order differential equations
• Kneser solutions
• Oscillatory solutions