## Oscillation criteria for half-linear second order differential equations.(English)Zbl 0872.34018

Some oscillation criteria are given for the second order nonlinear differential equation $[\Phi(u'(t))]'+ c(t)\Phi(u(t))=0,$ where $$c(t)$$ is a continuous function on $$[0,\infty)$$ and $$\Phi:\mathbb{R}\to\mathbb{R}$$ is defined by $$\Phi(x)=|x|^{p-2}x$$ with $$p>1$$ a fixed real number. If $$p=2$$, then these results improve earlier oscillation criteria of Wintner, Hartman, Kamenev and Philos.

### MSC:

 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations