Oscillation theorems for fourth-order quasi-linear delay differential equations

In this paper, we deal with the asymptotic and oscillatory behavior of quasi-linear delay differential equations of fourth order. We first find new properties for a class of positive solutions of the studied equation, $ \mathcal{N}_{a} $. As an extension of the approach taken in [1], we establish a new criterion that guarantees that $ \mathcal{N}_{a} = \emptyset $. Then, we create a new oscillation criterion.