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

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F13%3APU102365" target="_blank" >RIV/00216305:26220/13:PU102365 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

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

Original language description

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.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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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)

Publication year

2013

Confidentiality

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

Name of the periodical

Journal of Applied Mathematics

ISSN

1337-6365

e-ISSN

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Volume of the periodical

5 (2012)

Issue of the periodical within the volume

2

Country of publishing house

SK - SLOVAKIA

Number of pages

8

Pages from-to

139-146

UT code for WoS article

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EID of the result in the Scopus database

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