On certain asymptotic class of solutions to second order linear q-difference equations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14410%2F12%3A00057291" target="_blank" >RIV/00216224:14410/12:00057291 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1088/1751-8113/45/5/055202" target="_blank" >http://dx.doi.org/10.1088/1751-8113/45/5/055202</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/1751-8113/45/5/055202" target="_blank" >10.1088/1751-8113/45/5/055202</a>

Result language
angličtina
Original language name
On certain asymptotic class of solutions to second order linear q-difference equations
Original language description
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 ${q^k:kinN_0}$, $q>1$. The class of functions satisfying the relation $y(qt)/y(t)simomega(t)$ as $ttoinfty$ 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. Acomparison with existing results is made and some applications are given.
Czech name
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Czech description
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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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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
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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