Detail publikace

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

ŘEHÁK, P.

Anglický název

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

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

en

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova anglicky

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

Vydáno

01.12.2018

Nakladatel

Elsevier

Místo

USA

ISSN

0096-3003

Ročník

338

Číslo

-

Strany od–do

487–506

Počet stran

20

BIBTEX


@article{BUT150007,
  author="Pavel {Řehák},
  title="The Karamata integration theorem on time scales and its applications in dynamic and difference equations",
  year="2018",
  volume="338",
  number="-",
  month="December",
  pages="487--506",
  publisher="Elsevier",
  address="USA",
  issn="0096-3003"
}