Representation of solutions of a solvable nonlinear difference equation of second order

Stević Stevo and Iričanin Bratislav and Kosmala Witold and Šmarda Zdeněk: Representation of solutions of a solvable nonlinear difference equation of second order. (2018)

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We present a representation of well-defined solutions to the following nonlinear second-order difference equation xn+1 = a + b xn c xnxn−1 , n ∈ N0, where parameters a, b, c, and initial values x−1 and x0 are complex numbers such that c 6= 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.

Item Type: Journal
Publication full: Electronic journal of qualitative theory of differential equations
Date: 2018
Number: 95
ISSN: 1417-3875
Page Range: pp. 1-18
DOI: 10.14232/ejqtde.2018.1.95
Uncontrolled Keywords: Másodrendű differenciálegyenlet
Additional Information: Bibliogr.: p. 15-18. ; összefoglalás angol nyelven
Date Deposited: 2019. Jan. 25. 11:54
Last Modified: 2020. Jul. 29. 12:29

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