Some Oscillation Criteria for a Class of Third-Order Delay Differential Equations

Abstract

In this paper, we study oscillatory properties of solutions to a class of third-order differential equation a t r t x ′ t ′ α ′ + p t r t x ′ t ′ α + q t f x σ t = 0 , where f x / x β ≥ k > 0 and α and β are quotients of odd positive integers. By using the generalized Riccati technique, we obtain some oscillation and asymptotic criteria when α ≥ β and α < β . Finally, some examples are given to show the effectiveness of the criteria obtained.