A Philos-Type Oscillation Criteria for Fourth-Order Neutral Differential Equations

Some sufficient conditions are established for the oscillation of fourth order neutraldifferential equations of the form􀀀r (t) (z000 (t))a 0+ q (t) xb (s (t)) = 0, where z (t) := x (t) +p (t) x (t (t)). By using the technique of Riccati transformation and integral averaging method,we get conditions to ensure oscillation of solutions of this equation. Symmetry ideas are ofteninvisible in these studies, but they help us decide the right way to study them, and to show us thecorrect direction for future developments. Moreover, the importance of the obtained conditions isillustrated via some examples.