q-Karamata functions and second order q-difference equations
The result's identifiers
Result code in 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>
Alternative codes found
RIV/00216305:26220/11:PU91909 RIV/00216224:14410/11:00050560
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
q-Karamata functions and second order q-difference equations
Original language 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 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
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GAP201%2F10%2F1032" target="_blank" >GAP201/10/1032: Difference equations and dynamic equations on time scales III</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Electronic Journal of Qualitative Theory of Differential Equations.
ISSN
1417-3875
e-ISSN
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Volume of the periodical
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Issue of the periodical within the volume
24
Country of publishing house
HU - HUNGARY
Number of pages
20
Pages from-to
1-20
UT code for WoS article
000289152400001
EID of the result in the Scopus database
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