Detail publikace

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

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

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.

Klíčová slova

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

Autoři

ŘEHÁK, P.

Vydáno

24. 5. 2017

ISSN

0022-247X

Periodikum

Journal of Mathematical Analysis and Application

Ročník

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 Application",
  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"
}