A remark on the linearization technique in half-linear oscillation theory

Abstract

We show that oscillatory properties of the half-linear second order differential equation $(r(t)\Phi(x'))'+c(t)\Phi(x)=0,\qquad\Phi(x)=|x|^{p-2}x,\quad p\gt 1,$ can be investigated via oscillatory properties of a certain associated second order linear differential equation. In contrast to paper [6], we do not need to distinguish between the cases $p\ge 2$ and $p\in (1,2]$. Our results also improve the oscillation and nonoscillation criteria given in [4].