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

0343477 - MÚ 2011 RIV CZ eng J - Článek v odborném periodiku
Řehák, Pavel
A role of the coefficient of the differential term in qualitative theory of half-linear equations.
Mathematica Bohemica. Roč. 135, č. 2 (2010), s. 151-162. ISSN 0862-7959
Grant CEP: GA AV ČR KJB100190701
Grant ostatní: GA ČR(CZ) GA201/07/0145
Výzkumný záměr: CEZ:AV0Z10190503
Klíčová slova: half-linear dynamic equation * time scale * transformation * comparison theorem * oscillation criteria
Kód oboru RIV: BA - Obecná matematika
http://www.dml.cz/handle/10338.dmlcz/140692

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 sophisicated modifications of the Riccati type technique, which are supplemented by some new observations.
Trvalý link: http://hdl.handle.net/11104/0185947