Abstract
In the paper, we study the oscillation of fourth-order delay differential equations, the present authors used a Riccati transformation and the comparison technique for the fourth order delay differential equation, and that was compared with the oscillation of the certain second order differential equation. Our results extend and improve many well-known results for oscillation of solutions to a class of fourth-order delay differential equations. Some examples are also presented to test the strength and applicability of the results obtained.
Highlights
The problem of the oscillation of higher and fourth order differential equations have been widely studied by many authors, who have provided many techniques used for obtaining oscillatory criteria for higher and fourth order differential equations
The authors of this paper used the comparison technique for the fourth order delay differential equation and that was compared with the oscillation of certain second order differential equation
To the best of our knowledge, there is nothing known about the oscillation of (1) under the assumption (2), our primary goal is to fill this gap by presenting simple criteria for the oscillation of all solutions of (1) by using the generalized Riccati transformations and comparison technique, so the main advantage of studying (1) essentially lies in the direct application of the well-known Kiguradze lemma [23] (Lemma 1)
Summary
The problem of the oscillation of higher and fourth order differential equations have been widely studied by many authors, who have provided many techniques used for obtaining oscillatory criteria for higher and fourth order differential equations. Agarwal et al [1] and the present authors in [18] used the comparison technique for the fourth order delay differential equation h γ i0 m ( y ) z ( n −1) ( y ). The authors of this paper used the comparison technique for the fourth order delay differential equation and that was compared with the oscillation of certain second order differential equation. As usual and without loss of generality, we can deal only with eventually positive solutions of (1)
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