Publication detail

Asymptotics of perturbed discrete Euler equations in the critical case

ŘEHÁK, P.

English title

Asymptotics of perturbed discrete Euler equations in the critical case

Type

journal article in Web of Science

Language

en

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 in English

Euler difference equation; Asymptotic behavior; Regular variation

Released

15.04.2021

Publisher

ACADEMIC PRESS INC ELSEVIER SCIENCE

Location

SAN DIEGO

ISSN

0022-247X

Volume

496

Number

2

Pages from–to

1–9

Pages count

9

BIBTEX


@article{BUT167822,
  author="Pavel {Řehák},
  title="Asymptotics of perturbed discrete Euler equations in the critical case",
  year="2021",
  volume="496",
  number="2",
  month="April",
  pages="1--9",
  publisher="ACADEMIC PRESS INC ELSEVIER SCIENCE",
  address="SAN DIEGO",
  issn="0022-247X"
}