Detail publikačního výsledku

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

ŘEHÁK, P.

Originální název

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

Anglický název

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

Druh

Článek WoS

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

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

Klíčová slova v angličtině

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

Autoři

ŘEHÁK, P.

Rok RIV

2019

Vydáno

01.12.2018

Nakladatel

Elsevier

Místo

USA

ISSN

0096-3003

Periodikum

APPLIED MATHEMATICS AND COMPUTATION

Svazek

338

Číslo

-

Stát

Spojené státy americké

Strany od

487

Strany do

506

Strany počet

20

URL

https://doi.org/10.1016/j.amc.2018.06.023

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"
}