An asymptotic analysis of nonoscillatory solutions of q-difference equations via q-regular variation
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F17%3APU123809" target="_blank" >RIV/00216305:26210/17:PU123809 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jmaa.2017.05.034" target="_blank" >https://doi.org/10.1016/j.jmaa.2017.05.034</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2017.05.034" target="_blank" >10.1016/j.jmaa.2017.05.034</a>
Alternative languages
Result language
angličtina
Original language name
An asymptotic analysis of nonoscillatory solutions of q-difference equations via q-regular variation
Original language description
We do a thorough asymptotic analysis of nonoscillatory solutions of the $q$-difference equation $D_q(r(t)D_q y(t))+p(t)y(qt)=0$ considered on the lattice ${q^k:kinmathbb{N}_0}$, $q>1$. We classify the solutions according to various aspects that take into account their asymptotic behavior. We show relations among the asymptotic classes. For every positive solution we establish asymptotic formulae. Several discrepancies are revealed, when comparing the results with their existing differential equations or difference equations counterparts; however, it should be noted that many of our observations in the $q$-case have not their continuous or discrete analogies yet. Important roles in our considerations are played by the theory of $q$-regular variation and various transformations. The results are illustrated by examples.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Mathematical Analysis and Application
ISSN
0022-247X
e-ISSN
1096-0813
Volume of the periodical
454
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
54
Pages from-to
829-882
UT code for WoS article
000404425000023
EID of the result in the Scopus database
2-s2.0-85019631990