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 \[ \begin{split} (r(t)|u'(t)|^{\alpha-1}u'(t))' + q_0(t)|u[\tau_0(t)]|^{\alpha-1}u[\tau_0(t)] + q_1(t)|u[\tau_1(t)]|^{\beta-1}u[\tau_1(t)]\\ + q_2(t)|u[\tau_2(t)]|^{\gamma-1}u[\tau_2(t)]=0,\end{split} \]
where \(\gamma>\alpha>\beta>0\). Obtained criteria generalize earlier ones.


34K11 Oscillation theory of functional-differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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