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Oscillation solutions to third order half-linear neutral differential equations with “maxima”. (English) Zbl 1310.34091

Summary: We study the oscillation of solutions to the third order half-linear neutral differential equations with “maxima” \[ (a(t)((x(t)+p(t)x(\sigma(t)))'')^\alpha)'+q(t)\underset{[\tau(t), t]}\max x^\alpha(s)=0, \,\,t\geq t_0\geq0, \] where \(\alpha\) is the ratio of odd positive integers and \(\int^t_{t_{0}}a^{-1/\alpha}(t)dt=\infty\). Examples are given to illustrate the main results.

MSC:

34K11 Oscillation theory of functional-differential equations
34K40 Neutral functional-differential equations
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