In this paper, we investigate the oscillatory behavior of second-order neutral delay differential equations with a canonical operator of the form ( a ( x ) ( v ′ ( x ) ) m ) ′ + C ( x , u ( φ ( x ) ) ) = 0. We introduce new monotonicity properties of the non-oscillatory solutions of these equations, which are then used to linearize the equations and derive new oscillatory criteria. The presented results significantly improve upon existing criteria.
Temtek et al. (Wed,) studied this question.