SOME GENERALIZATIONS IN THEORY OF RAPID VARIATION ON TIME SCALES AND ITS APPLICATION IN DYNAMIC EQUATIONS

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F12%3APU99419" target="_blank" >RIV/00216305:26220/12:PU99419 - 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 APPLICATION 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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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
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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