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@article{873838,
author = {Řehák, Pavel},
article_location = {Bratislava},
article_number = {2},
doi = {http://dx.doi.org/10.2478/s12175-010-0009-7},
keywords = {dynamic equation; time scale; half-linear equation; (non)oscillation criteria; Hille-Nehari criteria; Kneser criteria; critical constant; oscillation constant; Hardy inequality},
language = {eng},
issn = {0139-9918},
journal = {Mathematica Slovaca},
title = {A critical oscillation constant as a variable of time scales for half-linear dynamic equations},
volume = {60},
year = {2010}
}
TY - JOUR
ID - 873838
AU - Řehák, Pavel
PY - 2010
TI - A critical oscillation constant as a variable of time scales for half-linear dynamic equations
JF - Mathematica Slovaca
VL - 60
IS - 2
SP - 237-256
EP - 237-256
PB - Slovak Academy of Sciences
SN - 01399918
KW - dynamic equation
KW - time scale
KW - half-linear equation
KW - (non)oscillation criteria
KW - Hille-Nehari criteria
KW - Kneser criteria
KW - critical constant
KW - oscillation constant
KW - Hardy inequality
N2 - We present criteria of Hille-Nehari type for the half-linear dynamic equation on time scales. As a particular important case we get that there is a a (sharp) critical constant which may be different from what is known from the continuous case, and its value depends on the graininess of a time scale and on the coefficient at the differential term. As applications we state criteria for strong (non)oscillation, examine generalized Euler type equations, and establish criteria of Kneser type. Examples from q-calculus, a Hardy type inequality with weights, and further possibilities for study are presented as well. Our results unify and extend many existing results from special cases, and are new even in the well-studied discrete case.
ER -
ŘEHÁK, Pavel. A critical oscillation constant as a variable of time scales for half-linear dynamic equations. \textit{Mathematica Slovaca}. Bratislava: Slovak Academy of Sciences, 2010, roč.~60, č.~2, s.~237-256. ISSN~0139-9918. Dostupné z: https://dx.doi.org/10.2478/s12175-010-0009-7.
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