A note on oscillation of second-order delay differential equations

Abstract

The purpose of this paper is to study the second-order half-linear delay differential equation r ( t ) y ′ ( t ) α ′ + q ( t ) y α ( τ ( t ) ) = 0 under the condition ∫ ∞ r − 1 ∕ α ( t ) d t < ∞ . Contrary to most existing results, oscillation of the studied equation is attained via only one condition. A particular example of Euler type equation is provided in order to illustrate the significance of our main results.