Detail publikačního výsledku

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

VÍTOVEC, J.

Originální název

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

Anglický název

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

Druh

Článek recenzovaný mimo WoS a Scopus

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.

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

VÍTOVEC, J.

Rok RIV

2014

Vydáno

15.01.2013

ISSN

1337-6365

Periodikum

Journal of Applied Mathematics

Svazek

5 (2012)

Číslo

2

Stát

Slovenská republika

Strany od

139

Strany do

146

Strany počet

8

BibTex

@article{BUT97750,
  author="Jiří {Vítovec}",
  title="Some generalizations in theory of rapid variation on time scales and its applications in dynamic equations",
  journal="Journal of Applied Mathematics",
  year="2013",
  volume="5 (2012)",
  number="2",
  pages="139--146",
  issn="1337-6365"
}