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VÍTOVEC, J.
Originální název
SOME GENERALIZATIONS IN THEORY OF RAPID VARIATION ON TIME SCALES AND ITS APPLICATION IN DYNAMIC EQUATIONS
Typ
článek ve sborníku ve WoS nebo Scopus
Jazyk
angličtina
Originální abstrakt
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.
Klíčová slova
Rapidly varying function, regularly varying function, regularly bounded function, time scale, half-linear dynamic equation.
Autoři
Rok RIV
2012
Vydáno
10. 2. 2012
ISBN
978-80-89313-58-7
Kniha
Aplimat 2012
Strany od
213
Strany do
220
Strany počet
8
BibTex
@inproceedings{BUT93412, author="Jiří {Vítovec}", title="SOME GENERALIZATIONS IN THEORY OF RAPID VARIATION ON TIME SCALES AND ITS APPLICATION IN DYNAMIC EQUATIONS", booktitle="Aplimat 2012", year="2012", pages="213--220", isbn="978-80-89313-58-7" }