A note on asymptotics and nonoscillation of linear $q$-difference equations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14410%2F12%3A00057377" target="_blank" >RIV/00216224:14410/12:00057377 - isvavai.cz</a>
Alternative codes found
RIV/67985840:_____/12:00376946
Result on the web
—
DOI - Digital Object Identifier
—

Result language
angličtina
Original language name
A note on asymptotics and nonoscillation of linear $q$-difference equations
Original language description
We study the linear second order $q$-difference equation $ y(q^2t)+a(t)y(qt)+b(t)y(t)=0 $ on the $q$-uniform lattice ${q^k:kinN_0}$ with $q>1$, where $b(t)ne0$. We establish various conditions guaranteeing the existence of solutions satisfying certain estimates resp. (non)oscillation of all solutions resp. $q$-regular boundedness of solutions resp. $q$-regular variation of solutions. Such results may provide quite precise information about their asymptotic behavior. Some of our results generalize existing Kneser type criteria and asymptotic formulas, which were stated for the equation $D_q^2y(qt)+p(t)y(qt)=0$, $D_q$ being the Jackson derivative. In the proofs however we use an original approach.
Czech name
—
Czech description
—

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

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

Name of the periodical
Electronic Journal of Qualitative Theory of Differential Equations
ISSN
1417-3875
e-ISSN
—
Volume of the periodical
neuveden
Issue of the periodical within the volume
4.5.2012
Country of publishing house
HU - HUNGARY
Number of pages
12
Pages from-to
1-12
UT code for WoS article
—
EID of the result in the Scopus database
—

Similar results(10)