q-Karamata functions and second order q-difference equations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F11%3A00374109" target="_blank" >RIV/67985840:_____/11:00374109 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216305:26220/11:PU91909 RIV/00216224:14410/11:00050560

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

q-Karamata functions and second order q-difference equations

Popis výsledku v původním jazyce

In this paper we introduce and study q-rapidly varying functions on the lattice q(N0) := {q(k) : k is an element of N(0)}, q > 1, which naturally extend the recently established concept of q-regularly varying functions. These types of functions togetherform the class of the so-called q-Karamata functions. The theory of q-Karamata functions is then applied to half-linear q-difference equations to get information about asymptotic behavior of nonoscillatory solutions. The obtained results can be seen as q-versions of the existing ones in the linear and half-linear differential equation case. However two important aspects need to be emphasized. First, a new method of the proof is presented. This method is designed just for the q-calculus case and turns out to be an elegant and powerful tool also for the examination of the asymptotic behavior to many other q-difference equations, which then may serve to predict how their (trickily detectable) continuous counterparts look like. Second, our

Název v anglickém jazyce

q-Karamata functions and second order q-difference equations

Popis výsledku anglicky

In this paper we introduce and study q-rapidly varying functions on the lattice q(N0) := {q(k) : k is an element of N(0)}, q > 1, which naturally extend the recently established concept of q-regularly varying functions. These types of functions togetherform the class of the so-called q-Karamata functions. The theory of q-Karamata functions is then applied to half-linear q-difference equations to get information about asymptotic behavior of nonoscillatory solutions. The obtained results can be seen as q-versions of the existing ones in the linear and half-linear differential equation case. However two important aspects need to be emphasized. First, a new method of the proof is presented. This method is designed just for the q-calculus case and turns out to be an elegant and powerful tool also for the examination of the asymptotic behavior to many other q-difference equations, which then may serve to predict how their (trickily detectable) continuous counterparts look like. Second, our

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GAP201%2F10%2F1032" target="_blank" >GAP201/10/1032: Diferenční rovnice a dynamické rovnice na ,,time scales'' III</a><br>

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2011

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Electronic Journal of Qualitative Theory of Differential Equations.

ISSN

1417-3875

e-ISSN

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Svazek periodika

-

Číslo periodika v rámci svazku

24

Stát vydavatele periodika

HU - Maďarsko

Počet stran výsledku

20

Strana od-do

1-20

Kód UT WoS článku

000289152400001

EID výsledku v databázi Scopus

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