About: Some generalizations in theory of rapid variation on time scales and its applications in dynamic equations

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	In this paper we introduce a new definition of rapidly varying function on time scales. Unlike the recently studied concept of rapid variation, this new concept is more general and naturally extends and complements the already established class of rapidly varying functions. We prove some of its properties and show the relation between this new type of definition and recently introduced classical Karamata type of definition of rapid variation on time scales. Note that the theory of rapid variation on time scales unifies the existing theories from continuous and discrete cases. As an application, we establish necessary and sufficient conditions for all positive solutions of the second order half-linear dynamic equations on time scales to be rapidly varying. In this paper we introduce a new definition of rapidly varying function on time scales. Unlike the recently studied concept of rapid variation, this new concept is more general and naturally extends and complements the already established class of rapidly varying functions. We prove some of its properties and show the relation between this new type of definition and recently introduced classical Karamata type of definition of rapid variation on time scales. Note that the theory of rapid variation on time scales unifies the existing theories from continuous and discrete cases. As an application, we establish necessary and sufficient conditions for all positive solutions of the second order half-linear dynamic equations on time scales to be rapidly varying. (en)
Title	Some generalizations in theory of rapid variation on time scales and its applications in dynamic equations Some generalizations in theory of rapid variation on time scales and its applications in dynamic equations (en)
skos:prefLabel	Some generalizations in theory of rapid variation on time scales and its applications in dynamic equations Some generalizations in theory of rapid variation on time scales and its applications in dynamic equations (en)
skos:notation	RIV/00216305:26220/13:PU102365!RIV14-GA0-26220___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GAP201/10/1032), Z(MSM0021630503), Z(MSM0021630529)
http://linked.open...iv/cisloPeriodika	2
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Vítovec, Jiří
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Vysoké učení technické v Brně / Fakulta elektrotechniky a komunikačních technologií
http://linked.open...dnocenehoVysledku	106322
http://linked.open...ai/riv/idVysledku	RIV/00216305:26220/13:PU102365
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Rapidly varying function, regularly varying function, regularly bounded function, time scale, half-linear dynamic equation. (en)
http://linked.open.../riv/klicoveSlovo	time scale Rapidly varying function half-linear dynamic equation. regularly bounded function regularly varying function
http://linked.open...odStatuVydavatele	SK - Slovenská republika
http://linked.open...ontrolniKodProRIV	[62A867125AD0]
http://linked.open...i/riv/nazevZdroje	Journal of Applied Mathematics
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Difference equations and dynamic equations on time scales III
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	5 (2012)
http://linked.open...iv/tvurceVysledku	Vítovec, Jiří
http://linked.open...n/vavai/riv/zamer	Nové trendy v mikroelektronických systémech a nanotechnologiích (MIKROSYN) Inteligentní systémy v automatizaci
issn	1337-6365
number of pages	8 (xsd:int)
http://localhost/t...ganizacniJednotka	26220

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