Oscillation of Second Order Nonlinear Impulsive Neutral Differential Equations

This article studies the sufficient conditions for the oscillation of second order impulsive nonlinear neutral differential equations of the form: $$\begin{aligned} (E) {\left\{ \begin{array}{ll} [u(t)+q(t)u(t-\alpha )]''+\varphi (t)f(u(t-\beta ))=0, \quad t\ne \delta _{k},~t\ge t_{0},\\ u(\delta ^{+}_{k})=M_k(u(\delta _{k})),\quad k\in {\mathbb {N}},\\ u'(\delta ^{+}_{k})=N_k(u'(\delta _{k})),\quad k\in {\mathbb {N}}, \end{array}\right. } \end{aligned}$$ where \(0 0\) for all \(u\ne 0\).