Authors: Stević, Stevo 
Iričanin, Bratislav
Šmarda, Zdenĕk
Title: Note on bounded solutions to nonhomogenous linear difference equations
Journal: Electronic Journal of Differential Equations
Volume: 2017
Issue Date: 14-Nov-2017
Rank: M21
ISSN: 1072-6691
URL: https://ejde.math.txstate.edu/Volumes/2017/286/stevic.pdf
Abstract: 
By using a solvability method along with the contraction mapping principle quite recently has been presented an interesting method for showing the existence of a unique bounded solution to a nonhomogenous linear second-order difference equation on the set of nonnegative integers. It is a natural question if the combination of the method and principle can be applied in showing the existence of bounded solutions to some higher-order generalizations of the equation. Here, among others, we give a positive answer to the question for the case of a nonhomogenous linear difference equation of third order. Moreover, the equation is studied on the whole integer domain ℤ.
Keywords: Bounded solution | Contraction mapping principle | Integer domain | Nonhomogeneous linear difference equation
Publisher: Texas State University
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 
Brno University of Technology, Project FEKT-S-17-4225

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