Oscillation and asymptotic behaviour of a higher-order nonlinear neutral-type functional differential equation with oscillating coefficients (Q554986)

Summary: We study the oscillation of bounded solutions of higher-order nonlinear neutral delay differential equations of the following type: \[ [y(t) + p(t)f(y(\tau(t)))]^{(n)} + q(t)h(y(\sigma(t))) = 0,\quad t \geq t_0,\quad t \in \mathbb R, \] where \(p \in C([t_0, \infty), \mathbb R)\), \(\lim_{t \rightarrow \infty}p(t) = 0\), \(q\in C([t_0, \infty)\), \(\mathbb R^+)\), \(\tau, \sigma\in C([t_0, \infty), \mathbb R)\), \(\tau(t), \sigma(t) < t\), \(\lim_{t \rightarrow \infty} \tau(t), \sigma(t) = \infty\), and \(f, h \in C(\mathbb R, \mathbb R)\). We obtain sufficient conditions for the oscillation of all solutions of this equation.