Publication detail

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

VÍTOVEC, J.

Original Title

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

English Title

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

Type

conference paper

Language

en

Original Abstract

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.

English abstract

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.

Keywords

Rapidly varying function, regularly varying function, regularly bounded function, time scale, half-linear dynamic equation.

RIV year

2012

Released

10.02.2012

ISBN

978-80-89313-58-7

Book

Aplimat 2012

Pages from

213

Pages to

220

Pages count

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"
}