Authors: | Stević, Stevo | Title: | Representations of solutions to linear and bilinear difference equations and systems of bilinear difference equations | Journal: | Advances in Difference Equations | Volume: | 2018 | Issue: | 1 | Issue Date: | 1-Dec-2018 | Rank: | M21 | ISSN: | 1687-1847 | DOI: | 10.1186/s13662-018-1930-2 | Abstract: | We represent general solution to a homogeneous linear difference equation of second order in terms of a specially chosen solution to the equation and apply it to get a representation of general solution to the bilinear difference equation in terms of a solution to an associate difference equation of second order, considerably generalizing some recent results in an elegant way. We also present the corresponding representations for some systems of bilinear difference equations. Many historical notes not so known to wide audience are also presented, and we offer an answer to an open question regarding the attribution of the bilinear difference equation. |
Keywords: | Bilinear difference equation | General solution | History of difference equations | Linear difference equation | Representation of solutions | System of bilinear difference equations | Publisher: | Springer Link | Project: | Modulation of intracellular energy balance-controlling signalling pathways in therapy of cancer and neuro-immuno-endocrine disorders 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 |
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