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Oscillation of second-order delay differential equations with mixed nonlinearities. (English) Zbl 1171.34338

The authors study the oscillatory behavior of delay differential equations with mixed nonlinearities

$\begin{array}{c}\left(r\left(t\right)|{u}^{\text{'}}{\left(t\right)|}^{\alpha -1}{u}^{\text{'}}{\left(t\right)\right)}^{\text{'}}+{q}_{0}\left(t\right)|u\left[{\tau }_{0}\left(t\right)\right]{|}^{\alpha -1}u\left[{\tau }_{0}\left(t\right)\right]+{q}_{1}\left(t\right){|u\left[{\tau }_{1}\left(t\right)\right]|}^{\beta -1}u\left[{\tau }_{1}\left(t\right)\right]\hfill \\ \hfill +{q}_{2}\left(t\right){|u\left[{\tau }_{2}\left(t\right)\right]|}^{\gamma -1}u\left[{\tau }_{2}\left(t\right)\right]=0,\end{array}$

where $\gamma >\alpha >\beta >0$. Obtained criteria generalize earlier ones.

##### MSC:
 34K11 Oscillation theory of functional-differential equations 34C10 Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
##### References:
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