Oscillation criteria for a class of nonlinear fourth order neutral differential equations

Abstract

In this paper, sufficient conditions are obtained for oscillation of a class of nonlinear fourth order mixed neutral differential equations of the form

$$\left( {\frac{1} {{a\left( t \right)}}\left( {\left( {y\left( t \right) + p\left( t \right)y\left( {t - \tau } \right)} \right)^{\prime \prime } } \right)^\alpha } \right)^{\prime \prime } = q\left( t \right)f\left( {y\left( {t - \sigma _1 } \right)} \right) + r\left( t \right)g\left( {y\left( {t + \sigma _2 } \right)} \right)$$

((E))

under the assumption

$$\int\limits_0^\infty {\left( {a\left( t \right)} \right)^{\tfrac{1} {\alpha }} dt} = \infty .$$

where α is a ratio of odd positive integers. (E) is studied for various ranges of p(t).