Publication details

A role of the coefficient of the differential term in qualitative theory of half-linear equations

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Year of publication 2010
Type Article in Periodical
Magazine / Source Mathematica Bohemica
MU Faculty or unit

Faculty of Education

Field General mathematics
Keywords half-linear dynamic equation; time scale; transformation; comparison theorem; oscillation criteria
Description The aim of this contribution is to study the role of the coefficient r at the differential term in the qualitative theory of the half-linear dynamic equation. We discuss sign and smoothness conditions posed on r, (non)availability of some transformations, and mainly we show how the behavior of r, along with the behavior of the graininess of the time scale, affect some comparison results and (non)oscillation criteria. At the same time we provide a survey of recent results acquired by sophisticated modifications of the Riccati type technique, which are supplemented by some new observations.
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