Oscillation Test for Second-Order Differential Equations with Several Delays

Abstract

In this paper, the oscillatory properties of certain second-order differential equations of neutral type are investigated. We obtain new oscillation criteria, which guarantee that every solution of these equations oscillates. Further, we get conditions of an iterative nature. These results complement and extend some beforehand results obtained in the literature. In order to illustrate the results we present an example.

Some Oscillatory Criteria for Second-Order Emden–Fowler Neutral Delay Differential Equations

“…These results expanded the range of the neutral coefficient p(t) in [11,17,20]. Abdelnaser et al [10] studied the oscillation of the following second-order Emden-Fowler equation under the canonical case…”

“…By view of α = 4 and β = 2, the oscillation criteria of [10,13,18,19,22,23,26] cannot be applied to Equation (56) because they are different equations, and the oscillation criteria of [21,[27][28][29] cannot be applied to Equation (56) because p(t) > 1.…”