On the oscillation of higher-order half-linear delay differential equations

In this note, we study the oscillatory behavior of the following higher-order half-linear delay differential equation ( r ( t ) ( x ( n − 1 ) ( t ) ) α ) ′ + q ( t ) x β ( τ ( t ) ) = 0 , t ≥ t 0 , where we assume ∫ t 0 ∞ 1 r 1 / α ( t ) d t < ∞ . An example is given to illustrate the main results.