Publication detail

q-Karamata functions and second order q-difference equations

VÍTOVEC, J. ŘEHÁK, P.

Original Title

q-Karamata functions and second order q-difference equations

English Title

q-Karamata functions and second order q-difference equations

Type

journal article

Language

en

Original Abstract

In this paper we introduce and study q-rapidly varying functions, which naturally extend the recently established concept of q-regularly varying functions. These types of functions together form the class of the so-called q-Karamata functions. The theory of q-Karamata functions is then applied to half-linear q-difference equations to get information about asymptotic behavior of nonoscillatory solutions. The obtained results can be seen as q-versions of the existing ones in the linear and half-linear differential equation case.

English abstract

In this paper we introduce and study q-rapidly varying functions, which naturally extend the recently established concept of q-regularly varying functions. These types of functions together form the class of the so-called q-Karamata functions. The theory of q-Karamata functions is then applied to half-linear q-difference equations to get information about asymptotic behavior of nonoscillatory solutions. The obtained results can be seen as q-versions of the existing ones in the linear and half-linear differential equation case.

Keywords

regularly varying functions; rapidly varying functions; q-difference equations; asymptotic behavior

RIV year

2011

Released

06.04.2011

Pages from

1

Pages to

20

Pages count

20

BibTex


@article{BUT44047,
  author="Jiří {Vítovec} and Pavel {Řehák}",
  title="q-Karamata functions and second order q-difference equations",
  annote="In this paper we introduce and study q-rapidly varying functions, which naturally extend the recently established concept of q-regularly varying functions. These types of functions together form the class of the so-called q-Karamata functions. The theory of q-Karamata functions is then applied to half-linear q-difference equations to get information about asymptotic behavior of nonoscillatory solutions. The obtained results can be seen as q-versions of the existing ones in the linear and half-linear differential equation case.",
  chapter="44047",
  journal="Electronic Journal of Qualitative Theory of Differential Equations",
  number="4",
  volume="24 (2011)",
  year="2011",
  month="april",
  pages="1--20",
  type="journal article"
}