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

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
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 $\{q^k:k\in\N_0\}$ 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. 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. (en)
Title	A note on asymptotics and nonoscillation of linear $q$-difference equations A note on asymptotics and nonoscillation of linear $q$-difference equations (en)
skos:prefLabel	A note on asymptotics and nonoscillation of linear $q$-difference equations A note on asymptotics and nonoscillation of linear $q$-difference equations (en)
skos:notation	RIV/00216224:14410/12:00057377!RIV13-GA0-14410___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GAP201/10/1032), Z(AV0Z10190503)
http://linked.open...iv/cisloPeriodika	4.5.2012
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Řehák, Pavel
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Masarykova univerzita / Pedagogická fakulta
http://linked.open...dnocenehoVysledku	120439
http://linked.open...ai/riv/idVysledku	RIV/00216224:14410/12:00057377
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	q-difference equation; asymptotic behavior; nonoscillation (en)
http://linked.open.../riv/klicoveSlovo	asymptotic behavior q-difference equation nonoscillation
http://linked.open...odStatuVydavatele	HU - Maďarsko
http://linked.open...ontrolniKodProRIV	[84F86A574A83]
http://linked.open...i/riv/nazevZdroje	Electronic Journal of Qualitative Theory of Differential Equations
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Difference equations and dynamic equations on time scales III
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	neuveden
http://linked.open...iv/tvurceVysledku	Řehák, Pavel
http://linked.open...n/vavai/riv/zamer	Rozvoj a prohloubení obecných matematických poznatků a jejich užití v dalších vědních oborech a v praxi
issn	1417-3875
number of pages	12 (xsd:int)
http://localhost/t...ganizacniJednotka	14410

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