Oscillation criteria for third-order nonlinear functional differential equations

In this work, we are concerned with oscillation of third-order nonlinear functional differential equations of the form ( r 2 ( t ) ( r 1 ( t ) y ′ ) ′ ) ′ + p ( t ) y ′ + q ( t ) f ( y ( g ( t ) ) ) = 0 . By using a Riccati type transformation and integral averaging technique, we establish some new sufficient conditions under which every solution y ( t ) either oscillates or converges to zero as t → ∞ . ones from the known works in the literature, our results are applicable to nonlinear functional differential equations of the above form when f ( u ) = | u | α − 1 u , α > 0 .