General k-Dimensional Solvable Systems of Difference Equations

Stević, Stevo

doi:10.3390/sym10010008

Cited by 2 publications

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“…The research of solvability of nonlinear systems of difference equations in this direction culminated with a quite general result on theoretical solvability proved in Stević …”

Section: Introductionmentioning

confidence: 98%

Two‐dimensional solvable system of difference equations with periodic coefficients

Stević

2019

Math Methods in App Sciences

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We show that the following two-dimensional system of difference equations:where (a n ) n∈N 0 , (b n ) n∈N 0 , (c n ) n∈N 0 , and (d n ) n∈N 0 are periodic sequences, is solvable, considerably extending some results in the literature. In the case when all these four sequences are periodic with period 2 or with period 3, we present closed-form formulas for the general solutions to the corresponding systems of difference equations. Some comments regarding theoretical and practical solvability of the system, connected to the value of the period of the sequences, aregiven. KEYWORDSclosed-form formula, solvable system, system of difference equations, system with periodic coefficients MSC CLASSIFICATIONwhere t 1 and t 2 are the zeros of t 2 + t + (in this case is t 1 ≠ t 2 ).Math Meth Appl Sci. 2019;42:6757-6774. wileyonlinelibrary.com/journal/mma

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“…The research of solvability of nonlinear systems of difference equations in this direction culminated with a quite general result on theoretical solvability proved in Stević …”

Section: Introductionmentioning

confidence: 98%

Two‐dimensional solvable system of difference equations with periodic coefficients

Stević

2019

Math Methods in App Sciences

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“…For more studied, see previous works. [9][10][11][12][13][14][15][16][17][18][19][20][21] There are many forms and types of rational difference equations which can be studied in different cases; for example, Stevi ć et al 22 solved the next rational difference equations w n+1 = w n−h w n−i 𝛼 w n−𝑗 + 𝛽 w n−k .…”

Section: Introductionmentioning

confidence: 99%

Qualitative behavior and solution of a system of three‐dimensional rational difference equations

Elsayed

Alshareef

Alzahrani

2022

Math Methods in App Sciences

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In this paper, we construct the solutions expressions for a system of three‐dimensional nonlinear difference equations Rn+1=a1Tn−1Sn−1Rn−1+Sn−1+Tn−1,Sn+1=a2Tn−1Rn−1Rn−1+Sn−1+Tn−1,Tn+1=a3Rn−1Sn−1Rn−1+Sn−1+Tn−1. In addition, we prove some properties of the proposed system such as boundedness and periodicity of the positive solutions and the global asymptotic stability of the equilibrium points. Finally, we present some numerical examples in order to illustrate the theoretical results.

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General k-Dimensional Solvable Systems of Difference Equations

Abstract: Abstract:The solvability of a k-dimensional system of difference equations of interest, which extends several recently studied ones, is investigated. A general sufficient condition for the solvability of the system is given, considerably extending some recent results in the literature.

Cited by 2 publications

References 42 publications

Two‐dimensional solvable system of difference equations with periodic coefficients

Two‐dimensional solvable system of difference equations with periodic coefficients

Qualitative behavior and solution of a system of three‐dimensional rational difference equations

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