About: q-Karamata functions and second order q-difference equations

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	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 together form 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 results show that q(N0) is a very natural setting for the theory of q-rapidly and q-regularly varying functions and its applications, and reveal some interesting phenomena, which are not known from the continuous theory. 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 together form 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 results show that q(N0) is a very natural setting for the theory of q-rapidly and q-regularly varying functions and its applications, and reveal some interesting phenomena, which are not known from the continuous theory. (en)
Title	q-Karamata functions and second order q-difference equations q-Karamata functions and second order q-difference equations (en)
skos:prefLabel	q-Karamata functions and second order q-difference equations q-Karamata functions and second order q-difference equations (en)
skos:notation	RIV/67985840:_____/11:00374109!RIV12-AV0-67985840
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GAP201/10/1032), Z(AV0Z10190503), Z(MSM0021630503)
http://linked.open...iv/cisloPeriodika	24
http://linked.open...vai/riv/dodaniDat	2012
http://linked.open...aciTvurceVysledku	Řehák, Pavel
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Matematický ústav AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	225347
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/11:00374109
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	regularly varying functions; rapidly varying functions; q-difference equations (en)
http://linked.open.../riv/klicoveSlovo	q-difference equations rapidly varying functions regularly varying functions
http://linked.open...odStatuVydavatele	HU - Maďarsko
http://linked.open...ontrolniKodProRIV	[5B208155A157]
http://linked.open...i/riv/nazevZdroje	Electronic Journal of Qualitative Theory of Differential Equations.
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Difference equations and dynamic equations on time scales III
http://linked.open...UplatneniVysledku	2011
http://linked.open...v/svazekPeriodika	-
http://linked.open...iv/tvurceVysledku	Řehák, Pavel Vítovec, J.
http://linked.open...ain/vavai/riv/wos	000289152400001
http://linked.open...n/vavai/riv/zamer	Rozvoj a prohloubení obecných matematických poznatků a jejich užití v dalších vědních oborech a v praxi Nové trendy v mikroelektronických systémech a nanotechnologiích (MIKROSYN)
issn	1417-3875
number of pages	20 (xsd:int)

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