Oscillation Criteria of Fourth-Order Differential Equations with Delay Terms

Abstract

The aim of this paper is to derive oscillation criteria of the following fourth-order differential equation with delay term rxz′′′xγ′+∑i=1nqixfzηix=0, under the assumption ∫x0∞r−1/γsds=∞. The results are based on comparison with the oscillatory behaviour of second-order delay equations and the generalised Riccati transformation. Not only do the provided theorems provide an entirely new technique but also they vastly improve on a number of previously published conclusions. We give three examples to illustrate our findings.