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Statements

Subject Item
n2:RIV%2F67985840%3A_____%2F11%3A00374109%21RIV12-AV0-67985840
rdf:type
skos:Concept n18:Vysledek
dcterms: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.
dcterms:title
q-Karamata functions and second order q-difference equations q-Karamata functions and second order q-difference equations
skos:prefLabel
q-Karamata functions and second order q-difference equations q-Karamata functions and second order q-difference equations
skos:notation
RIV/67985840:_____/11:00374109!RIV12-AV0-67985840
n18:predkladatel
n19:ico%3A67985840
n4:aktivita
n11:Z n11:P
n4:aktivity
P(GAP201/10/1032), Z(AV0Z10190503), Z(MSM0021630503)
n4:cisloPeriodika
24
n4:dodaniDat
n8:2012
n4:domaciTvurceVysledku
n5:5894484
n4:druhVysledku
n16:J
n4:duvernostUdaju
n10:S
n4:entitaPredkladatele
n15:predkladatel
n4:idSjednocenehoVysledku
225347
n4:idVysledku
RIV/67985840:_____/11:00374109
n4:jazykVysledku
n17:eng
n4:klicovaSlova
regularly varying functions; rapidly varying functions; q-difference equations
n4:klicoveSlovo
n7:q-difference%20equations n7:rapidly%20varying%20functions n7:regularly%20varying%20functions
n4:kodStatuVydavatele
HU - Maďarsko
n4:kontrolniKodProRIV
[5B208155A157]
n4:nazevZdroje
Electronic Journal of Qualitative Theory of Differential Equations.
n4:obor
n12:BA
n4:pocetDomacichTvurcuVysledku
1
n4:pocetTvurcuVysledku
2
n4:projekt
n14:GAP201%2F10%2F1032
n4:rokUplatneniVysledku
n8:2011
n4:svazekPeriodika
-
n4:tvurceVysledku
Vítovec, J. Řehák, Pavel
n4:wos
000289152400001
n4:zamer
n13:AV0Z10190503 n13:MSM0021630503
s:issn
1417-3875
s:numberOfPages
20