Title
qKaramatine funkcije i asimptotska svojstva rešenja nelinearnih qdiferencnih jednačina
Creator
Đorđević, Katarina S., 1991
CONOR:
80066569
Copyright date
2021
Object Links
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AutorstvoNekomercijalnoBez prerade 3.0 Srbija (CC BYNCND 3.0)
License description
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Language
Serbian
CobissID
Theses Type
Doktorska disertacija
description
Datum odbrane: 17.12.2021.
Other responsibilities
predsednik komisije
Rajković, Predrag
član komisije
Jovanović, Miljana
član komisije
Ilić, Velimir
Academic Expertise
Prirodnomatematičke nauke
Academic Title

University
Univerzitet u Nišu
Faculty
Prirodnomatematički fakultet
Group
Odsek za matematiku i informatiku
Alternative title
qKaramata funktions and asymptotic behavior of solutions of nonlinear qdifference equations
Publisher
[K. S. Đorđević]
Format
VI, 112 str.
description
Bibliografija: str. 103112;
Biobibliografski podaci:: str [113114].
description
Differential and difference equations
Abstract (en)
The purpose of the doctoral dissertation is to determine the conditions for the existence and to examine in detail the asymptotic properties of solutions of the second order nonlinear qdifference equations, with an application of the theory of qregular variation.
The halflinear qdifference equation was analyzed in the framework of qregular variation. Necessary and sufficient conditions for the existence of qregularly varying solutions of the halflinear q difference equation were obtained. Moreover, sufficient conditions for all eventually positive solutions to be qregularly varying were examined. In cases where this is possible, the application of qKaramata’s integration theorem and properties of qregularly varying functions have been used to determine the precise asymptotic formula of different types of solutions, which accurately describes the behavior of these solutions in long time intervals, which is of special importance from the point of view of application. The obtained results in the qcalculus were compared with the known results in the continuous and the discrete case, but also, they were used to obtain new results in the discrete asymptotic theory.
The sublinear second order qdifference equation of EmdenFowler type was also analyzed in the framework of qregularly varying functions. Assuming that the coefficients of this equation are qregularly varying functions, necessary and sufficient conditions for the existence of strongly increasing and strongly decreasing solutions, as well as their asymptotic representations at infinity, have been determined. Moreover, it was shown that all qregularly varying solutions of the same regularity index have the same asymptotic representation at infinity. The obtained results enabled the complete structure of the set of qregularly varying solutions to be presented.
Authors Key words
Nelinearne qdiferencne jednačine, Polulinearna qdiferencna jednačina, Pravilno promenljivi nizovi, qpravilno promenljive funkcije, Neoscilatorna rešenja, Asimptotsko ponašanje rešenja
Authors Key words
Nonlinear qdifference equations, Halflinear qdifference equation, Regularly varying sequences, qregularly varying functions, Nonoscillatory solutions, Asymptotic behavior of solutions
Classification
517.5:517.962.24(043.3)
Subject
P130
Type
Tekst
Abstract (en)
The purpose of the doctoral dissertation is to determine the conditions for the existence and to examine in detail the asymptotic properties of solutions of the second order nonlinear qdifference equations, with an application of the theory of qregular variation.
The halflinear qdifference equation was analyzed in the framework of qregular variation. Necessary and sufficient conditions for the existence of qregularly varying solutions of the halflinear q difference equation were obtained. Moreover, sufficient conditions for all eventually positive solutions to be qregularly varying were examined. In cases where this is possible, the application of qKaramata’s integration theorem and properties of qregularly varying functions have been used to determine the precise asymptotic formula of different types of solutions, which accurately describes the behavior of these solutions in long time intervals, which is of special importance from the point of view of application. The obtained results in the qcalculus were compared with the known results in the continuous and the discrete case, but also, they were used to obtain new results in the discrete asymptotic theory.
The sublinear second order qdifference equation of EmdenFowler type was also analyzed in the framework of qregularly varying functions. Assuming that the coefficients of this equation are qregularly varying functions, necessary and sufficient conditions for the existence of strongly increasing and strongly decreasing solutions, as well as their asymptotic representations at infinity, have been determined. Moreover, it was shown that all qregularly varying solutions of the same regularity index have the same asymptotic representation at infinity. The obtained results enabled the complete structure of the set of qregularly varying solutions to be presented.
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