A role of the coefficient of the differential term in qualitative theory of half-linear equations
Mathematica Bohemica (2010)
- Volume: 135, Issue: 2, page 151-162
- ISSN: 0862-7959
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topŘehák, Pavel. "A role of the coefficient of the differential term in qualitative theory of half-linear equations." Mathematica Bohemica 135.2 (2010): 151-162. <http://eudml.org/doc/38119>.
@article{Řehák2010,
abstract = {The aim of this contribution is to study the role of the coefficient $r$ in the qualitative theory of the equation $(r(t)\Phi (y^\{\Delta \}))^\{\Delta \} +p(t)\Phi (y^\{\sigma \})=0$, where $\Phi (u)=|u|^\{\alpha -1\}\mathop \{\rm sgn\}u$ with $\alpha >1$. 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.},
author = {Řehák, Pavel},
journal = {Mathematica Bohemica},
keywords = {half-linear dynamic equation; time scale; transformation; comparison theorem; oscillation criteria; half-linear dynamic equation; time scale; transformation; comparison theorem; oscillation criteria},
language = {eng},
number = {2},
pages = {151-162},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A role of the coefficient of the differential term in qualitative theory of half-linear equations},
url = {http://eudml.org/doc/38119},
volume = {135},
year = {2010},
}
TY - JOUR
AU - Řehák, Pavel
TI - A role of the coefficient of the differential term in qualitative theory of half-linear equations
JO - Mathematica Bohemica
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 135
IS - 2
SP - 151
EP - 162
AB - The aim of this contribution is to study the role of the coefficient $r$ in the qualitative theory of the equation $(r(t)\Phi (y^{\Delta }))^{\Delta } +p(t)\Phi (y^{\sigma })=0$, where $\Phi (u)=|u|^{\alpha -1}\mathop {\rm sgn}u$ with $\alpha >1$. 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.
LA - eng
KW - half-linear dynamic equation; time scale; transformation; comparison theorem; oscillation criteria; half-linear dynamic equation; time scale; transformation; comparison theorem; oscillation criteria
UR - http://eudml.org/doc/38119
ER -
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