Publication detail

The Karamata integration theorem on time scales and its applications in dynamic and difference equations

ŘEHÁK, P.

Original Title

The Karamata integration theorem on time scales and its applications in dynamic and difference equations

English Title

The Karamata integration theorem on time scales and its applications in dynamic and difference equations

Type

journal article in Web of Science

Language

en

Original Abstract

We derive a time scale version of the well-known result from the theory of regular variation, namely the Karamata integration theorem. We show an application of this theorem in asymptotic analysis of linear second order dynamic equations. We obtain a classification and asymptotic formulae for all (positive) solutions, which unify, extend, and improve the existing results. In addition, we utilize these results, in combination with a transformation between equations on different time scales, to study the critical double-root case in linear difference equations. This leads to solving open problems posed in the literature.

English abstract

We derive a time scale version of the well-known result from the theory of regular variation, namely the Karamata integration theorem. We show an application of this theorem in asymptotic analysis of linear second order dynamic equations. We obtain a classification and asymptotic formulae for all (positive) solutions, which unify, extend, and improve the existing results. In addition, we utilize these results, in combination with a transformation between equations on different time scales, to study the critical double-root case in linear difference equations. This leads to solving open problems posed in the literature.

Keywords

Karamata integration theorem; regular variation; time scale; dynamic equation; asymptotic formulae

Released

01.12.2018

Publisher

Elsevier

Location

USA

Pages from

487

Pages to

506

Pages count

20

URL

BibTex


@article{BUT150007,
  author="Pavel {Řehák}",
  title="The Karamata integration theorem on time scales and its applications in dynamic and difference equations",
  annote="We derive a time scale version of the well-known result from the theory of regular variation, namely the Karamata integration theorem. 
We show an application of this theorem in asymptotic analysis of linear second order dynamic equations. We obtain a classification and asymptotic formulae for all (positive) solutions, which unify, extend, and improve the existing results. In addition, we utilize these results, in combination with a transformation between equations on different time scales, to study the critical double-root case in linear difference equations. This leads to solving open problems posed in the literature.",
  address="Elsevier",
  chapter="150007",
  doi="10.1016/j.amc.2018.06.023",
  howpublished="print",
  institution="Elsevier",
  number="-",
  volume="338",
  year="2018",
  month="december",
  pages="487--506",
  publisher="Elsevier",
  type="journal article in Web of Science"
}