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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.

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