Detail výsledku

Regular variation on measure chains

VÍTOVEC, J.; ŘEHÁK, P. Regular variation on measure chains. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, vol. 72, no. 1, p. 439-448. ISSN: 0362-546X.
Typ
článek v časopise
Jazyk
anglicky
Autoři
Vítovec Jiří, Mgr., Ph.D., UMAT (FEKT)
Řehák Pavel, prof. Mgr., Ph.D.
Abstrakt

In this paper we show how the recently introduced concept of regular variation on time scales (or measure chains) is related to a Karamata type definition. We also present characterization theorems and an embedding theorem for regularly varying functions defined on suitable subsets of reals. We demonstrate that for a reasonable theory of regular variation on time scales, certain additional condition on a graininess is needed, which cannot be omitted. We establish a number of elementary properties of regularly varying functions. As an application, we study the asymptotic properties of solution to second order dynamic equations.

Klíčová slova

Regularly varying function; Regularly varying sequence; Measure chain; Time scale; Embedding theorem; Representation theorem; Second order dynamic equation; Asymptotic properties

Rok
2010
Strany
439–448
Časopis
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, roč. 72, č. 1, ISSN 0362-546X
BibTeX 
@article{BUT50468,
  author="Jiří {Vítovec} and Pavel {Řehák}",
  title="Regular variation on measure chains",
  journal="NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS",
  year="2010",
  volume="72",
  number="1",
  pages="439--448",
  issn="0362-546X"
}
Pracoviště
Ústav matematiky (UMAT)
Nahoru