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A note on asymptotics and nonoscillation of linear q-difference equations
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SYSNO ASEP 0376946 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Ostatní články Title A note on asymptotics and nonoscillation of linear q-difference equations Author(s) Řehák, Pavel (MU-W) RID, SAI, ORCID Source Title Electronic Journal of Qualitative Theory of Differential Equations. - : University of Szeged - ISSN 1417-3875
Roč. 12, May 04 (2012), s. 1-12Number of pages 12 s. Publication form Online - E Action Colloquium on the Qualitative Theory of Differential Equations /9./ Event date 28.06.2011-01.07.2011 VEvent location Szeged Country HU - Hungary Event type WRD Language eng - English Country HU - Hungary Keywords q-difference equation ; oscillation ; asymptotic behavior Subject RIV BA - General Mathematics CEZ AV0Z10190503 - MU-W (2005-2011) Annotation 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 $/{q^k:k/in/N_0/}$ 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2013
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