Unbounded oscillation criteria for fourth order neutral differential equations of non-canonical type

Abstract

Abstract In this work, sufficient conditions are established for oscillation of all unbounded solutions of a class of fourth order neutral differential equations of the form ( r ( t ) ( y ( t ) + p ( t ) y ( t − τ ) ) ″ ) ″ + q ( t ) G ( y ( t − α ) ) − h ( t ) H ( y ( t − σ ) ) = 0 $$\begin{array}{}\displaystyle (r(t)(y(t)+p(t)y(t-\tau))'')''+q(t)G(y(t-\alpha))-h(t)H(y(t-\sigma)) = 0\end{array} $$ under the non-canonical type assumption ∫ 0 ∞ t r ( t ) d t < ∞ $$\begin{array}{}\displaystyle \int\limits_{0}^{\infty}\frac{t}{r(t)}{\rm d} t \lt \infty\end{array} $$ for various ranges of p(t) with ∣p(t)∣ < ∞.