Asymptotic properties of solutions to second order dynamic equations in the framework of regular variation with emphasis on q-calculus case

0351219 - MÚ 2011 CZ eng A - Abstrakt
Řehák, Pavel
Asymptotic properties of solutions to second order dynamic equations in the framework of regular variation with emphasis on q-calculus case.
Abstract book of CDEIT 2010. Brno: Masarykova univerzita, 2010 - (Došlá, Z.; Mařík, R.; Hilscher, R.; Šremr, J.). s. 69-71. ISBN 978-80-210-5289-5.
[Colloquium on differential equations and integration theory. 14.10.2010-17.10.2010, Křtiny]
Výzkumný záměr: CEZ:AV0Z10190503
Klíčová slova: second order dynamic equations * q-calculus
Kód oboru RIV: BA - Obecná matematika
http://www.math.muni.cz/~cdeit/abstracts/rehak.pdf

We focus primarily on the q-calculus case, where we work on the q-uniform lattice qN0 := fqk : k 2 N0g. For a basic material on this calculus see [1, 5, 6]. See also [3] for the calculus on time scales which somehow contains q-calculus. The theory of q-calculus is very extensive with many aspects; some people speak about different tongues of q-calculus. In our consideration we follow essentially its “time scale dialect”. Concerning the definition of q-regularly varying functions, we may follow general theory and define it in terms of the Jackson derivative or to provide a Karamata type definition.
Trvalý link: http://hdl.handle.net/11104/0191019