Authors: Stević, Stevo 
Iričanin, Bratislav
Kosmala, Witold
Šmarda, Zdeněk
Title: Note on the bilinear difference equation with a delay
Journal: Mathematical Methods in the Applied Sciences
Volume: 41
Issue: 18
First page: 9349
Last page: 9360
Issue Date: 1-Dec-2018
Rank: M21
ISSN: 0170-4214
DOI: 10.1002/mma.5293
Abstract: 
A representation formula for the general solution to a higher-order rational difference equation has been given recently in this journal. The formula was proved by the method of induction without giving any theoretical explanation related to it. Here we show how the corresponding representation formula for the general solution to a general higher-order rational difference equation, that is, to the bilinear difference equation with a delay, is obtained in an elegant way. We also give some theoretical explanations related to the representation, as well as some explanations related to such types of difference equations. The corresponding representation for a system of bilinear difference equations with delay is also presented.
Keywords: bilinear difference equation | difference equation with interlacing indices | general solution
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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