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Oscillation theorems for second-order superlinear neutral differential equations. (English) Zbl 1313.34193
Summary: The purpose of this paper is to investigate the oscillation of second-order neutral differential equations of the form \[ \bigl (r(t)| z'(t)| ^{\alpha -1}z'(t)\bigr)' +q(t)| x(\sigma (t))| ^{\alpha -1}x\bigl (\sigma (t)\bigr)=0, \tag{E} \] where \(z(t)=x(t)+p(t)x\bigl (\tau (t)\bigr)\). The obtained comparison principles essentially simplify the examination of the studied equations. Further, our results extend and improve the results in the literature.

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