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q-Karamata functions and second order q-difference equations

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F11%3A00374109" target="_blank" >RIV/67985840:_____/11:00374109 - isvavai.cz</a>

  • Alternative codes found

    RIV/00216305:26220/11:PU91909 RIV/00216224:14410/11:00050560

  • Result on the web

  • DOI - Digital Object Identifier

Alternative languages

  • Result language

    angličtina

  • Original language name

    q-Karamata functions and second order q-difference equations

  • Original language description

    In this paper we introduce and study q-rapidly varying functions on the lattice q(N0) := {q(k) : k is an element of N(0)}, q > 1, which naturally extend the recently established concept of q-regularly varying functions. These types of functions togetherform 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. However two important aspects need to be emphasized. First, a new method of the proof is presented. This method is designed just for the q-calculus case and turns out to be an elegant and powerful tool also for the examination of the asymptotic behavior to many other q-difference equations, which then may serve to predict how their (trickily detectable) continuous counterparts look like. Second, our

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

    <a href="/en/project/GAP201%2F10%2F1032" target="_blank" >GAP201/10/1032: Difference equations and dynamic equations on time scales III</a><br>

  • Continuities

    Z - Vyzkumny zamer (s odkazem do CEZ)

Others

  • Publication year

    2011

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Electronic Journal of Qualitative Theory of Differential Equations.

  • ISSN

    1417-3875

  • e-ISSN

  • Volume of the periodical

    -

  • Issue of the periodical within the volume

    24

  • Country of publishing house

    HU - HUNGARY

  • Number of pages

    20

  • Pages from-to

    1-20

  • UT code for WoS article

    000289152400001

  • EID of the result in the Scopus database