o:1732 Asymptotic representation of solutions of nonlinear differential and difference equations with regularly varying coefficients: doctoral dissertation Asimptotska reprezentacija rešenja nelinearnih diferencijalnih i diferencnih jednačina sa pravilno promenljivim koeficijentima : doctoral dissertation en 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 considered 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. Bibliografija: str. 143-154;Biografija sa bibliografijom: str. 155-156. Datum odbrane: 19.02.2021. Differential and difference equations 33902089 91552101 8235 91552100 33902089 2021-08-25T13:05:32.053Z 45 no 46 mentor Aleksandra B. 1988- Kapešić 2020 63 mentor Jelena Manojlović 2020 63 član komisije Dragan 1967- Đurčić 2020 63 član komisije Miljana D. 1965- Jovanović 2020 63 član komisije Ljubiša D. R. 1947- Kočinac 2020 VII, 156 str. 5544397 http://phaidrabg.bg.ac.rs/o:1732 no yes 4 2021-08-25T13:05:32.320Z 70 regularly varying functions, regularly varying sequences, asymptoticbehaviour of solutions, fourth order differential equation, nonlineardifference equations, systems of difference equations pravilno promenljive funkcije, pravilno promenljivi nizovi,asimptotsko ponašanje rešenja, diferencijalne jednačine četvrtogreda, nelinearne diferencne jednačine, sistemi diferencnihjednačina 517.928/.929(043.3) P130 1738 18A07 18A0701 2020