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Asymptotic representation of solutions of nonlinear differential and difference equations with regularly varying coefficients

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2021
Kapesic_Aleksandra_B.pdf (538.7Kb)
Doctoral_thesis_11452.pdf (5.287Mb)
Author
Kapešić, Aleksandra B.
Mentor
Manojlović, Jelena
Committee members
Đurčić, Dragan
Jovanović, Miljana D.
Kočinac, Ljubiša D. R.
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Abstract
In this dissertation, differential equations of the fourth order, difference equation of second order and cyclic systems of difference equations of second order are considered. In particular, assuming that coefficients of fourth order differential equation of Emden-Fowler type are generalized regularly varying functions, complete information about the existence of all possible intermediate regularly varying solutions and their accurate asymptotic behavior at infinity are given. The second order difference equation of Thomas-Fermy type is discussed in the framework of discrete regular variation and its strongly increasing and strongly decreasing solutions are examined in detail. Necessary and sufficient conditions for the existence of these solutions, as well as their asymptotic representations, have been determined. The obtained results enabled the complete structure of a set of regularly varying solutions to be presented. Cyclic systems of difference equations are conside...red as a natural generalization of second order difference equations. A full characterization of the limit behavior of all positive solutions is established. In particular, the asymptotic behavior of intermediate, as well as strongly increasing and strongly decreasing solutions is analyzed under the assumption that coefficients of the systems are regularly varying sequences and exact asymptotic formulas are derived for all these types of solutions. Also, the conditions for the existence of all types of positive solutions have been obtained.

Faculty:
Универзитет у Нишу, Природно-математички факултет
Date:
19-02-2021
Projects:
  • info:eu-repo/grantAgreement/MESTD/Basic Research (BR or ON)/174007/RS// (RS-174007)
Keywords:
regularly varying functions, regularly varying sequences, asymptotic behaviour of solutions, fourth order differential equation, nonlinear difference equations, systems of difference equations / pravilno promenljive funkcije, pravilno promenljivi nizovi, asimptotsko ponašanje rešenja, diferencijalne jednačine četvrtog reda, nelinearne diferencne jednačine, sistemi diferencnih jednačina
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Handle
https://hdl.handle.net/21.15107/rcub_nardus_18560
URI
http://eteze.ni.ac.rs/application/showtheses?thesesId=8235
https://fedorani.ni.ac.rs/fedora/get/o:1732/bdef:Content/download
http://vbs.rs/scripts/cobiss?command=DISPLAY&base=70052&RID=33902089
https://nardus.mpn.gov.rs/handle/123456789/18560

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