Publication detail

Positive decreasing solutions of half-linear dynamic equations

VÍTOVEC, J.

Original Title

Positive decreasing solutions of half-linear dynamic equations

English Title

Positive decreasing solutions of half-linear dynamic equations

Type

conference paper

Language

en

Original Abstract

The aim of this contribution is to provide complete and precise information on asymptotic behaviour of all positive decreasing solutions of certain half-linear dynamic equation. We will show that these solutions are normalized regularly or rapidly varying if and only if the coeficient p satisfies certain integral conditions. Moreover, the index of regular variation will be shown to be related to the limit behaviour of the coefficient p. In addition to the theory of rapid variation we established a missing representation formula for rapidly varying functions on time scales.

English abstract

The aim of this contribution is to provide complete and precise information on asymptotic behaviour of all positive decreasing solutions of certain half-linear dynamic equation. We will show that these solutions are normalized regularly or rapidly varying if and only if the coeficient p satisfies certain integral conditions. Moreover, the index of regular variation will be shown to be related to the limit behaviour of the coefficient p. In addition to the theory of rapid variation we established a missing representation formula for rapidly varying functions on time scales.

Keywords

Regularly varying function; rapidly varying function; time scale; Representation theorem; half-linear dynamic equation

RIV year

2011

Released

19.05.2011

Publisher

Univerzita obrany

Location

Brno

ISBN

978-80-7231-779-0

Book

XXIX International Colloquium on the Management of the Educational Process. Proceedings.

Pages from

1

Pages to

9

Pages count

9

BibTex


@inproceedings{BUT72474,
  author="Jiří {Vítovec}",
  title="Positive decreasing solutions of half-linear dynamic equations",
  annote="The aim of this contribution is to provide complete and precise information on asymptotic behaviour of all positive decreasing solutions of certain half-linear dynamic equation. We will show that these solutions are normalized regularly or rapidly varying if and only if the coeficient p satisfies certain integral conditions. Moreover, the index of regular variation will be shown to be related to the limit behaviour of the coefficient p. In addition to the theory of rapid variation we established a missing representation formula for rapidly varying functions on time scales.",
  address="Univerzita obrany",
  booktitle="XXIX International Colloquium on the Management of the Educational Process. Proceedings.",
  chapter="72474",
  howpublished="print",
  institution="Univerzita obrany",
  year="2011",
  month="may",
  pages="1--9",
  publisher="Univerzita obrany",
  type="conference paper"
}