Authors: Stević, Stevo 
Iričanin, Bratislav
Kosmala, Witold
Šmarda, Zdeněk
Title: Solvability of a nonlinear fifth-order difference equation
Journal: Mathematical Methods in the Applied Sciences
Volume: 42
Issue: 5
First page: 1687
Last page: 1701
Issue Date: 30-Mar-2019
Rank: M21
ISSN: 0170-4214
DOI: 10.1002/mma.5467
Some formulas for well-defined solutions to four very special cases of a nonlinear fifth-order difference equation have been presented recently in this journal, where some of them were proved by the method of induction, some are only quoted, and no any theory behind the formulas was given. Here, we show in an elegant constructive way how the general solution to the difference equation can be obtained, from which the special cases very easily follow, which is also demonstrated here. We also give some comments on the local stability results on the special cases of the nonlinear fifth-order difference equation previously publish in this journal.
Keywords: general solution | linear first-order difference equation | nonlinear difference equation | solvability
Publisher: Wiley
Project: Modulation of intracellular energy balance-controlling signalling pathways in therapy of cancer and neuro-immuno-endocrine disorders 
Physical and functional effects of radiation interaction with electrotechnical and biological systems 
Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education 
Brno University of Technology, Project FEKT-S-17-4225

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