Asymptotic representation of solutions of nonlinear differential and difference equations with regularly varying coefficients
Author
Kapešić, Aleksandra B.Mentor
Manojlović, JelenaCommittee members
Đurčić, DraganJovanović, Miljana D.
Kočinac, Ljubiša D. R.
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Show full item recordAbstract
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 факултетDate:
19-02-2021Projects:
- Functional analysis, stochastic analysis and applications (RS-MESTD-Basic Research (BR or ON)-174007)