Oscillation and nonoscillation criteria for delay differential equations

Abstract:

Oscillation and nonoscillation criteria for the first-order delay differential equation \[ x’(t) + p(t)x(\tau (t)) = 0,\quad t \geq {t_0},\tau (t) < t,\] are established in the case where \[ \int _{\tau (t)}^t {p(s)ds \geq \frac {1}{e}\quad {\text {and}}\quad \lim \limits _{t \to \infty } \int _{\tau (t)}^t {p(s)ds = \frac {1}{e}.} } \]