Oscillation criteria for second-order superlinear neutral differential equations (Q535959)

Summary: Some oscillation criteria are established for the second-order superlinear neutral differential equation \[ (r(t)|z'(t)|^{\alpha-1} z'(t))'+f(t,x(\sigma(t)))=0,\quad t\geq t_0, \] where \(z(t)=x(t)+p(t)x(\tau(t))\), \(\tau(t)\geq t\), \(\sigma(t)\geq t\), \(p\in C([t_0,\infty), [0,p_0])\), and \(\alpha\geq 1\). Our results are based on the cases \(\int^\infty_{t_0} 1/r^{1/\alpha}(t)\, dt=\infty\) or \(\int^\infty_{t_0} 1/r^{1/\alpha}(t)\, dt< \infty\). Two examples are also provided to illustrate these results.