Leighton-Hille-Kneser-type oscillation criteria for Emden-Fowler neutral delay differential equations

Emden-Fowler differential equations have numerous applications in physics and engineering. In this article, we extended the classical Leighton, Hille, and Kneser types oscillation criteria for second-order linear differential equations to the second-order Emden-Fowler neutral delay differential equation

$${\left(r(t){\left|z^{\mathrm{\prime }}(t)\right|}^{\alpha -1}{z}^{\mathrm{\prime }}(t)\right)}^{\mathrm{\prime }}+q(t){\left|y(\sigma (t))\right|}^{\beta }\text{sgn}y(\sigma (t))=0,t\ge t_0,$$

where $z(t)=y(t)+p(t)y(\tau (t)).$ The criteria obtained extended and improved some well-known results reported in the literature. Moreover, several examples are provided to show the significance of the new findings.