Second order neutral delay differential equations: on oscillation via linearization

This paper investigates the oscillatory behavior of second-order neutral differential equations with a continuously distributed delay. New monotonic characteristics of non-oscillatory solutions of the considered neutral delay differential equation are established. We obtain new oscillation criteria by using these properties to linearize the problem and applying the comparison principle. The corresponding proofs are established under the canonical assumption. The results in this paper improve and generalize some known results in the existing works. Finally, numerical validation via illustrative examples are provided.