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 WoS

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.

Klíčová slova anglicky

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

Vydáno

2018-12-01

Nakladatel

Elsevier

Místo

USA

ISSN

0096-3003

Časopis

APPLIED MATHEMATICS AND COMPUTATION

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",
  journal="APPLIED MATHEMATICS AND COMPUTATION",
  year="2018",
  volume="338",
  number="-",
  pages="487--506",
  doi="10.1016/j.amc.2018.06.023",
  issn="0096-3003",
  url="https://doi.org/10.1016/j.amc.2018.06.023"
}