Kneser-type oscillation criteria for second-order half-linear delay differential equations

Abstract In the paper, we establish a variant of Kneser oscillation theorem for the second-order half-linear delay differential equation ( r ( t ) | y ′ ( t ) | α − 1 y ′ ( t ) ) ′ + q ( t ) | y ( τ ( t ) ) | α − 1 y ( τ ( t ) ) = 0 , t ≥ t 0 > 0 , under the assumption ∫ t 0 ∞ r − 1 / α ( s ) d s = ∞ , which improves a plenty of results reported in the literature. In case of α ≥ 1, the obtained criterion is sharp in the sense that the oscillation constant is optimal for the corresponding half-linear Euler type equation with delay, while the result for α