Oscillations of half-linear second order differential equations
Let \(\varphi:\mathbb{R}\to\mathbb{R}\) be defined by \(\varphi(s)=|s|^{p-2}s\), with \(p>1\) a fixed number. We extend Sturm's comparison theorem of the linear differential equation \[ {\textstyle {\frac{d}{dt}}} [r(t)u'(t)]+ c(t)u(t)=0 \] to the nonlinear differential equation \[ {\textstyle {\frac{d}{dt}}} \{r(t)\varphi(u'(t))\}+ c(t)\varphi(u(t))=0, \tag{E} \] by using the Wirtinger inequality. A Lyapunov inequality and some oscillation criteria of (E) are also given.
scientific article; zbMATH DE number 863653