Publication result detail

Asymptotics of perturbed discrete Euler equations in the critical case

ŘEHÁK, P.

Original Title

Asymptotics of perturbed discrete Euler equations in the critical case

English Title

Asymptotics of perturbed discrete Euler equations in the critical case

Type

WoS Article

Original Abstract

We consider the difference equation Delta(2)y(k) + p(k)y(k + 1) = 0 under the condition lim(k ->infinity) k(2)p(k) = 1/4; such a setting can cover various perturbations of the critical (double root) case in Euler type difference equations. We establish precise asymptotic formulae for all nonoscillatory solutions. An important role is played by the concept of the refined discrete regular variation, transformations of dependent and independent variable, and asymptotic theory of dynamic equations on time scales. (C) 2020 Elsevier Inc. All rights reserved.

English abstract

We consider the difference equation Delta(2)y(k) + p(k)y(k + 1) = 0 under the condition lim(k ->infinity) k(2)p(k) = 1/4; such a setting can cover various perturbations of the critical (double root) case in Euler type difference equations. We establish precise asymptotic formulae for all nonoscillatory solutions. An important role is played by the concept of the refined discrete regular variation, transformations of dependent and independent variable, and asymptotic theory of dynamic equations on time scales. (C) 2020 Elsevier Inc. All rights reserved.

Keywords

Euler difference equation; Asymptotic behavior; Regular variation

Key words in English

Euler difference equation; Asymptotic behavior; Regular variation

Authors

ŘEHÁK, P.

RIV year

2021

Released

15.04.2021

Publisher

ACADEMIC PRESS INC ELSEVIER SCIENCE

Location

SAN DIEGO

ISBN

0022-247X

Periodical

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Volume

496

Number

2

State

United States of America

Pages from

1

Pages to

9

Pages count

9

URL

https://doi.org/10.1016/j.jmaa.2020.124825

BibTex

@article{BUT167822,
  author="Pavel {Řehák}",
  title="Asymptotics of perturbed discrete Euler equations in the critical case",
  journal="JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS",
  year="2021",
  volume="496",
  number="2",
  pages="1--9",
  doi="10.1016/j.jmaa.2020.124825",
  issn="0022-247X",
  url="https://doi.org/10.1016/j.jmaa.2020.124825"
}