Authors: Stević, Stevo 
Alghamdi, Mohammed
Alotaibi, Abdullah
Elsayed, Elsayed
Title: On a class of solvable higher-order difference equations
Journal: Filomat
Volume: 31
Issue: 2
First page: 461
Last page: 477
Issue Date: 1-Jan-2017
Rank: M22
ISSN: 0354-5180
DOI: 10.2298/FIL1702461S
Abstract: 
Closed form formulas for well-defined solutions of the next difference equation (Formula prsented), where k ϵ ℕ, (an)nϵℕ0 and initial values x-i, i = (Formula prsented) are real numbers, are given. Long-term behavior of well-defined solutions of the equation when (an)nϵℕ0 and (bn)nϵℕ0are constant sequences is described in detail by using the formulas. We also describe the domain of undefinable solutions of the equation. Our results explain and considerably improve some recent results in the literature.
Keywords: Domain of undefinable solutions | Linear first order difference equation | Long-term behavior | Solvable difference equation
Publisher: Faculty of Sciences and Mathematics, University of Niš
Project: Deanship of Scientific Research (DSR) at King Abdulaziz University, Grant no. HiCi-33-130-36

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