Solvable three-dimensional system of higher-order nonlinear difference equations

Merve Kara ; Yasin Yazlik

Filomat, Tome 36 (2022) no. 10, p. 3449

Résumé

In this work, we indicate three-dimensional system of difference equations xn = ayn−k + dyn−kxn−k−l b̂xn−k−l + ĉzn−l , yn = αzn−k + δzn−k yn−k−l β̂yn−k−l + γ̂xn−l , zn = exn−k + hxn−kzn−k−l f̂ zn−k−l + 1̂yn−l , n ∈N0, where k and l are positive integers, the parameters a, b̂, ĉ, d, α, β̂, γ̂, δ, e, f̂ , 1̂, h and the initial values x− j, y− j, z− j j = 1, k + l, are non-zero real numbers, can be solved in closed form. In addition, we obtain explicit formulas for the well-defined solutions of the aforementioned system for the case l = 1. Also, the set of undefinable solutions of the system is found. Finally, an application about a three-dimensional system of difference equations is given.

Détail

DOI : 10.2298/FIL2210449K

Classification : 39A10, 39A20, 39A23
Keywords: Closed form, forbidden set, higher-order difference equation, system of difference equations