Detail publikace

Některá zobecnění v teorii rychlé variace na časových škálách a její aplikace v dynamických rovnicích

VÍTOVEC, J.

Originální název

SOME GENERALIZATIONS IN THEORY OF RAPID VARIATION ON TIME SCALES AND ITS APPLICATION IN DYNAMIC EQUATIONS

Český název

Některá zobecnění v teorii rychlé variace na časových škálách a její aplikace v dynamických rovnicích

Anglický název

SOME GENERALIZATIONS IN THEORY OF RAPID VARIATION ON TIME SCALES AND ITS APPLICATION IN DYNAMIC EQUATIONS

Typ

článek ve sborníku

Jazyk

en

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.

Český abstrakt

V tomto článku představíme nový typ definice rychlé variace na časových škálách. Narozdíl od nedávno studovaného konceptu rychlé variace, nový koncept je více obecný a přirozeně rozšiřuje a doplňuje již zavedenou třídu rychle se měnících funkcí. Dokážeme některé její vlastnosti a ukážeme vztah mezi touto nově zavedenou definicí a dříve představenou klasickou Karamatovou definicí rychlé variace na časových škálách.

Anglický 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.

Rok RIV

2012

Vydáno

10.02.2012

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",
  annote="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.",
  booktitle="Aplimat 2012",
  chapter="93412",
  howpublished="electronic, physical medium",
  year="2012",
  month="february",
  pages="213--220",
  type="conference paper"
}