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

Oscillation of Fourth-Order Delay Differential Equations

“…1: Our aim in the present paper is to employ the Riccatti technique to establish some new conditions for the oscillation of all solutions of (1.1). The results not only differ from the results obtained in [22] but also improve some of them. Some examples are considered to illustrate the main results.…”

“…It is easy to see that every solution of (3.2) is oscillatory due to Theorem 2.1. One of these solutions is x.t / D e t sin t: However, it follows from [22] (Corollary 2.1) that (3.2) may have nonoscillatory solutions x satisfying lim t !1 x.t / D 0: Hence, our results supplement and improve the results obtained in [22].…”

“…Agarwal, et al [7] and Zhang, et al [22] studied the oscillatory properties of the higher-order differential equation…”

Oscillatory Behavior of Higher-Order Delay Differential Equations

“…Hence every solution of (3.2) is oscillatory. However,theresults of [21] cannot confirm this conclusion. Then we can easily see that all assumptions of Corollary 2.1 are satisfied.…”

“…C.Zhang, et al [20] and Zhang, et al [21] consider the oscillatory properties of the higher-order differential equation…”