Oscillation of one kind of second order neutral delay differential equations (Q2019882)

Summary: This paper is dedicated to discussing the oscillation of the second order neutral delay differential equations \[ \big(r(t)(z'(t))^\alpha\big)'+q(t)f(x^\beta(\sigma(t)))=0, \] where \(z(t) = x(t) + p(t)x (\tau(t))\). Sufficient conditions are provided by Riccati transformation comparing with related first order differential inequalities and differential equations. Results obtained in this paper have extended and improved conclusions contained in other literatures. Several illustrative examples are presented.