Result Details

q-Karamata functions and second order q-difference equations

VÍTOVEC, J.; ŘEHÁK, P. q-Karamata functions and second order q-difference equations. Electronic Journal of Qualitative Theory of Differential Equations, 2011, vol. 24 (2011), no. 4, p. 1-20. ISSN: 1417-3875.
Type
journal article
Language
English
Authors
Vítovec Jiří, Mgr., Ph.D., UMAT (FEEC)
Řehák Pavel, prof. Mgr., Ph.D.
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

Published
2011
Pages
1–20
Journal
Electronic Journal of Qualitative Theory of Differential Equations, vol. 24 (2011), no. 4, ISSN 1417-3875
BibTeX 
@article{BUT44047,
  author="Jiří {Vítovec} and Pavel {Řehák}",
  title="q-Karamata functions and second order q-difference equations",
  journal="Electronic Journal of Qualitative Theory of Differential Equations",
  year="2011",
  volume="24 (2011)",
  number="4",
  pages="1--20",
  issn="1417-3875"
}
Departments
Department of Mathematics (UMAT)
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