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Open AccessFeature PaperArticle

Solvability of the Class of Two-Dimensional Product-Type Systems of Difference Equations of Delay-Type (1, 3, 1, 1)

by 1,2
1
Mathematical Institute of the Serbian Academy of Sciences, Knez Mihailova 36/III, 11000 Beograd, Serbia
2
Operator Theory and Applications Research Group, Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Academic Editor: Sergei D. Odintsov
Symmetry 2017, 9(10), 200; https://doi.org/10.3390/sym9100200
Received: 1 September 2017 / Revised: 21 September 2017 / Accepted: 21 September 2017 / Published: 25 September 2017
(This article belongs to the Special Issue Symmetry: Feature Papers 2017)
This paper essentially presents the last and important steps in the study of (practical) solvability of two-dimensional product-type systems of difference equations of the following form z n = α z n - k a w n - l b , w n = β w n - m c z n - s d , n N 0 , where k , l , m , s N , a , b , c , d Z , and where α , β and the initial values are complex numbers. It is devoted to the most complex case which has not been considered so far (the case k = l = s = 1 and m = 3 ). Closed form formulas for solutions to the system are found in all possible cases. The structure of the solutions to the system is considered in detail. The following five cases: (1) b = 0 ; (2) c = 0 ; (3) d = 0 ; (4) a c 0 ; (5) a = 0 , b c d 0 , are considered separately. Some of the situations appear for the first time in the literature. View Full-Text
Keywords: system of difference equations; product-type system; system solvable in closed form system of difference equations; product-type system; system solvable in closed form
MDPI and ACS Style

Stević, S. Solvability of the Class of Two-Dimensional Product-Type Systems of Difference Equations of Delay-Type (1, 3, 1, 1). Symmetry 2017, 9, 200.

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