New oscillatory criteria for higher-order nonlinear neutral delay differential equation

Abstract

In this paper, we consider the higher-order nonlinear neutral delay differential equation (1.1) ( x ( t ) − p ( t ) x ( t − τ ) ) ( n ) + f ( t , x ( σ ( t ) ) ) = 0 where n is an odd number and n ⩾ 3 , τ > 0 , p , σ ∈ C ( [ t 0 , ∞ ) , R + ) , σ ( t ) ⩽ t , lim t → ∞ σ ( t ) = ∞ , f ∈ C ( [ t 0 , ∞ ) × R , R ) , f ( t , u ) is nondecreasing in u .