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@article{975047,
author = {Řehák, Pavel},
article_location = {Velká Británie},
article_number = {5},
doi = {http://dx.doi.org/10.1088/1751-8113/45/5/055202},
keywords = {q-difference equation; asymptotic behavior; regular variation; oscillation},
language = {eng},
issn = {1751-8113},
journal = {Journal of Physics A: Mathematical and Theoretical},
title = {On certain asymptotic class of solutions to second order linear q-difference equations},
volume = {45},
year = {2012}
}
TY - JOUR
ID - 975047
AU - Řehák, Pavel
PY - 2012
TI - On certain asymptotic class of solutions to second order linear q-difference equations
JF - Journal of Physics A: Mathematical and Theoretical
VL - 45
IS - 5
SP - 1-19
EP - 1-19
PB - IOP Publishing
SN - 17518113
KW - q-difference equation
KW - asymptotic behavior
KW - regular variation
KW - oscillation
N2 - The paper deals with the linear second order $q$-difference equation $y(q^2t)+a(t)y(qt)+b(t)y(t)=0$, $b(t)\ne 0$, considered on $\{q^k:k\in\N_0\}$, $q>1$. The class of functions satisfying the relation $y(qt)/y(t)\sim\omega(t)$ as $t\to\infty$ for some function $\omega$ is introduced and studied. Sufficient and necessary conditions are established for the equation to have solutions in this class. Related results concerning estimates for solutions and (non)oscillation of all solutions are discussed. A comparison with existing results is made and some applications are given.
ER -
ŘEHÁK, Pavel. On certain asymptotic class of solutions to second order linear q-difference equations. \textit{Journal of Physics A: Mathematical and Theoretical}. Velká Británie: IOP Publishing, 2012, vol.~45, No~5, p.~1-19. ISSN~1751-8113. Available from: https://dx.doi.org/10.1088/1751-8113/45/5/055202.
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