A role of the coefficient of the differential term in qualitative theory of half-linear equations
| Authors | |
|---|---|
| Year of publication | 2010 |
| Type | Article in Periodical |
| Magazine / Source | Mathematica Bohemica |
| MU Faculty or unit | |
| Citation | |
| 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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