Oscillatory behavior of higher order neutral differential equation with multiple functional delays under derivative operator

Abstract

. In this article, we obtain sufficient conditions so that every solution of neutral delay differential equation oscillates or tends to zero as t → ∞ , where, n ≥ 1 is any positive integer, p i , r i ∈ C ( n ) ([0 , ∞ ) , R ) and p i are bounded for each i = 1 , 2 ,...,k . Further, f ∈ C ([0 , ∞ ) , R ), g , h , v , u ∈ C ([0 , ∞ ) , [0 , ∞ )), G and H ∈ C ( R , R ). The functional delays r i ( t ) ≤ t , g ( t ) ≤ t and h ( t ) ≤ t and all of them approach ∞ as t → ∞ . The results hold when u ≡ 0 and f ( t ) ≡ 0. This article extends, generalizes and improves some recent results, and further answers some unanswered questions from the literature.