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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F18%3APU129055" target="_blank" >RIV/00216305:26210/18:PU129055 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.amc.2018.06.023" target="_blank" >https://doi.org/10.1016/j.amc.2018.06.023</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.amc.2018.06.023" target="_blank" >10.1016/j.amc.2018.06.023</a>

Result language
angličtina
Original language name
The Karamata integration theorem on time scales and its applications in dynamic and difference equations
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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