Solvability of a Three-Dimensional System of Nonlinear Difference Equations

Authors : Merve KARA

Pages : 1-15

Doi:10.36753/mathenot.992987

View : 37 | Download : 11

Publication Date : 2022-03-01

Article Type : Research Paper

Abstract :In this paper, we solve the following three-dimensional system of difference equations x n = y n − 4 z n − 5 y n − 1 insert ignore into journalissuearticles values( a n + b n z n − 2 x n − 3 y n − 4 z n − 5 ); , y n = z n − 4 x n − 5 z n − 1 insert ignore into journalissuearticles values( α n + β n x n − 2 y n − 3 z n − 4 x n − 5 ); , z n = x n − 4 y n − 5 x n − 1 insert ignore into journalissuearticles values( A n + B n y n − 2 z n − 3 x n − 4 y n − 5 ); ,   n ∈ N 0 , xn=yn−4zn−5yn−1insert ignore into journalissuearticles values(an+bnzn−2xn−3yn−4zn−5);,yn=zn−4xn−5zn−1insert ignore into journalissuearticles values(αn+βnxn−2yn−3zn−4xn−5);,zn=xn−4yn−5xn−1insert ignore into journalissuearticles values(An+Bnyn−2zn−3xn−4yn−5);, n∈N0, where the sequences insert ignore into journalissuearticles values( a n ); n ∈ N 0 insert ignore into journalissuearticles values(an);n∈N0 , insert ignore into journalissuearticles values( b n ); n ∈ N 0 insert ignore into journalissuearticles values(bn);n∈N0 , insert ignore into journalissuearticles values( α n ); n ∈ N 0 insert ignore into journalissuearticles values(αn);n∈N0 , insert ignore into journalissuearticles values( β n ); n ∈ N 0 insert ignore into journalissuearticles values(βn);n∈N0 , insert ignore into journalissuearticles values( A n ); n ∈ N 0 insert ignore into journalissuearticles values(An);n∈N0 , insert ignore into journalissuearticles values( B n ); n ∈ N 0 insert ignore into journalissuearticles values(Bn);n∈N0 and the initial values x − j , y − j x−j,y−j , j = ¯ ¯¯¯¯¯¯ ¯ 1 , 5 j=1,5¯ , are real numbers. In addition, the constant coefficient of the mentioned system is solved in closed form. Finally, we also describe the forbidden set of solutions of the system of difference equations.
Keywords : system of difference equations, closed form, forbidden set

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