Authors: Stević, Stevo 
Iričanin, Bratislav
Kosmala, Witold
Šmarda, Zdeněk
Title: Representation of solutions of a solvable nonlinear difference equation of second order
Journal: Electronic Journal of Qualitative Theory of Differential Equations
Volume: 2018
Issue Date: 1-Jan-2018
Rank: M21
ISSN: 1417-3875
DOI: 10.14232/ejqtde.2018.1.95
We present a representation of well-defined solutions to the following nonlinear second-order difference equation (Formula Presented.) where parameters a, b, c, and initial values x –1 and x 0 are complex numbers such that c ≠ 0, in terms of the parameters, initial values, and a special solution to a thirdorder homogeneous linear difference equation with constant coefficients associated to the nonlinear difference equation, generalizing a recent result in the literature, completing the proof therein by using an essentially constructive method, and giving some theoretical explanations related to the method for solving the difference equation. We also give a more concrete representation of the solutions to the nonlinear difference equation by calculating the special solution to the third-order homogeneous linear difference equation in terms of the zeros of the characteristic polynomial associated to the linear difference equation.
Keywords: Linear difference equation | Nonlinear second-order difference equation | Representation of solutions | Solvable difference equation
Publisher: Bolyai Institute, University of Szeged
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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