Necessary and sufficient conditions for oscillation to second-order half-linear delay differential equations (Q2326931)

Some necessary and sufficient conditions for the oscillation of all solutions of second-order half-linear delay differential equations of the form \[ \left( r\left( x^{\prime }\right) ^{\gamma }\right) ^{\prime }\left( t\right) +q\left( t\right) x^{\alpha }\left( \tau \left( t\right) \right) =0 \] are obtained by considering two cases: \(\gamma >\alpha \) and \( \gamma <\alpha \) and under the assumption \(\int^{\infty }\frac{d\eta }{ r^{1/\gamma }\left( \eta \right) }=\infty \). Examples illustrate the results and the improvement achieved.