Electron. J. Diff. Equ., Vol. 2015 (2015), No. 169, pp. 1-20.

Solvable product-type system of difference equations of second order

Stevo Stevic, Mohammed A. Alghamdi, Abdullah Alotaibi, Elsayed M. Elsayed

Abstract:
We show that the system of difference equations
$$ z_{n+1}=\frac{w_n^a}{z_{n-1}^b},\quad w_{n+1}=\frac{z_n^c}{w_{n-1}^d},\quad n\in\mathbb{N}_0, $$
where $a,b,c,d\in\mathbb{Z}$, and initial values $z_{-1}, z_0, w_{-1}, w_0\in\mathbb{C}$, is solvable in closed form, and present a method for finding its solutions.

Submitted February 7, 2015. Published June 18, 2015.
Math Subject Classifications: 39A10, 39A20.
Key Words: Solvable system of difference equations; second-order system; product-type system; long-term behavior.

Show me the PDF file (321 KB), TEX file, and other files for this article.

Stevo Stevic
Mathematical Institute of the Serbian Academy of Sciences
Knez Mihailova 36/III, 11000 Beograd, Serbia
email: sstevic@ptt.rs
  Mohammed A. Alghamdi
Operator Theory and Applications Research Group
Department of Mathematics, Faculty of Science
King Abdulaziz University, P.O. Box 80203
Jeddah 21589, Saudi Arabia
email: proff-malghamdi@hotmail.com
  Abdullah Alotaibi
Operator Theory and Applications Research Group
Department of Mathematics, Faculty of Science
King Abdulaziz University, P.O. Box 80203
Jeddah 21589, Saudi Arabia
email: aalotaibi@kau.edu.sa
  Elsayed M. Elsayed
Department of Mathematics, Faculty of Science
King Abdulaziz University, P.O. Box 80203
Jeddah 21589, Saudi Arabia
email: emmelsayed@yahoo.com

Return to the EJDE web page