New oscillation criteria for linear delay differential equations (Q1125005)

This work provides sufficient conditions for the oscillation of all solutions to the first-order linear delay differential equation \[ x''(t)+p(t)x(r(t))=0, t\geq t_0, \] under the conditions: \(p(t)\geq 0\) is a piecewise continuous function, \(r(t)<t\) is strictly increasing on \([t_0, \infty)\) and \(\lim_{t\to \infty}r(t)=\infty\). As an application of these results the authors provide theorems on the oscillation of neutral differential equations.