Detail publikačního výsledku

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

ŘEHÁK, P.

Originální název

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

Anglický název

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

Druh

Článek WoS

Originální abstrakt

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 $\{q^k:k\in\mathbb{N}_0\}$, $q>1$. 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.

Anglický abstrakt

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 $\{q^k:k\in\mathbb{N}_0\}$, $q>1$. 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.

Klíčová slova

q-difference equation; nonoscillatory solution; monotone solution; asymptotic formula; regular variation

Klíčová slova v angličtině

q-difference equation; nonoscillatory solution; monotone solution; asymptotic formula; regular variation

Autoři

ŘEHÁK, P.

Rok RIV

2018

Vydáno

24.05.2017

ISSN

0022-247X

Periodikum

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Svazek

454

Číslo

2

Stát

Spojené státy americké

Strany od

829

Strany do

882

Strany počet

54

URL

https://doi.org/10.1016/j.jmaa.2017.05.034

BibTex

@article{BUT136766,
  author="Pavel {Řehák}",
  title="An asymptotic analysis of nonoscillatory solutions of q-difference equations via q-regular variation",
  journal="JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS",
  year="2017",
  volume="454",
  number="2",
  pages="829--882",
  doi="10.1016/j.jmaa.2017.05.034",
  issn="0022-247X",
  url="https://doi.org/10.1016/j.jmaa.2017.05.034"
}