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Oscillation criteria for second-order superlinear neutral differential equations. (English) Zbl 1217.34112
Summary: Some oscillation criteria are established for the second-order superlinear neutral differential equation $$(r(t)|z'(t)|^{\alpha-1} z'(t))'+f(t,x(\sigma(t)))=0,\quad t\ge t_0,$$ where $z(t)=x(t)+p(t)x(\tau(t))$, $\tau(t)\ge t$, $\sigma(t)\ge t$, $p\in C([t_0,\infty), [0,p_0])$, and $\alpha\ge 1$. Our results are based on the cases $\int^\infty_{t_0} 1/r^{1/\alpha}(t)\, dt=\infty$ or $\int^\infty_{t_0} 1/r^{1/\alpha}(t)\, dt< \infty$. Two examples are also provided to illustrate these results.

##### MSC:
 34K11 Oscillation theory of functional-differential equations 34K40 Neutral functional-differential equations
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