An asymptotic analysis of nonoscillatory solutions of q-difference equations via q-regular variation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F17%3APU123809" target="_blank" >RIV/00216305:26210/17:PU123809 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.jmaa.2017.05.034" target="_blank" >https://doi.org/10.1016/j.jmaa.2017.05.034</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jmaa.2017.05.034" target="_blank" >10.1016/j.jmaa.2017.05.034</a>

Jazyk výsledku

angličtina

Název v původním jazyce

An asymptotic analysis of nonoscillatory solutions of q-difference equations via q-regular variation

Popis výsledku v původním jazyce

We do a thorough asymptotic analysis of nonoscillatory solutions of the $q$-difference equation $D_q(r(t)D_q y(t))+p(t)y(qt)=0$ considered on the lattice ${q^k:kinmathbb{N}_0}$, $q>1$. We classify the solutions according to various aspects that take into account their asymptotic behavior. We show relations among the asymptotic classes. For every positive solution we establish asymptotic formulae. Several discrepancies are revealed, when comparing the results with their existing differential equations or difference equations counterparts; however, it should be noted that many of our observations in the $q$-case have not their continuous or discrete analogies yet. Important roles in our considerations are played by the theory of $q$-regular variation and various transformations. The results are illustrated by examples.

Název v anglickém jazyce

An asymptotic analysis of nonoscillatory solutions of q-difference equations via q-regular variation

Popis výsledku anglicky

We do a thorough asymptotic analysis of nonoscillatory solutions of the $q$-difference equation $D_q(r(t)D_q y(t))+p(t)y(qt)=0$ considered on the lattice ${q^k:kinmathbb{N}_0}$, $q>1$. We classify the solutions according to various aspects that take into account their asymptotic behavior. We show relations among the asymptotic classes. For every positive solution we establish asymptotic formulae. Several discrepancies are revealed, when comparing the results with their existing differential equations or difference equations counterparts; however, it should be noted that many of our observations in the $q$-case have not their continuous or discrete analogies yet. Important roles in our considerations are played by the theory of $q$-regular variation and various transformations. The results are illustrated by examples.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Mathematical Analysis and Application

ISSN

0022-247X

e-ISSN

1096-0813

Svazek periodika

454

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

54

Strana od-do

829-882

Kód UT WoS článku

000404425000023

EID výsledku v databázi Scopus

2-s2.0-85019631990