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

0343477 - MÚ 2011 RIV CZ eng J - Journal Article
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
R&D Projects: GA AV ČR KJB100190701
Grant - others:GA ČR(CZ) GA201/07/0145
Institutional research plan: CEZ:AV0Z10190503
Keywords : half-linear dynamic equation * time scale * transformation * comparison theorem * oscillation criteria
Subject RIV: BA - General Mathematics
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.
Permanent Link: http://hdl.handle.net/11104/0185947