Results 21 to 30 of about 2,105 (253)

ON A SOLVABLE SYSTEM OF NON-LINEAR DIFFERENCE EQUATIONS WITH VARIABLE COEFFICIENTS

Journal of Science and Arts, 2021
In this paper, we show that the system of difference equations can be solved in the closed form. Also, we determine the forbidden set of the initial values by using the obtained formulas. Finally, we obtain periodic solutions of aforementioned system.
Kara, Merve, Yazlık, Yasin
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On a solvable class of product-type systems of difference equations

Filomat, 2017
It is shown that the following class of systems of difference equations zn+1 = ?zanwbn, wn+1 = ?wcnzdn-2, n ? N0, where a,b,c,d ? Z, ?, ?, z-2, z-1, z0,w0 ? C \ {0}, is solvable, continuing our investigation of classification of solvable product-type systems with two dependent variables.
Stević, Stevo, Iričanin, Bratislav, Šmarda, Zdeněk   +2 more
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New solvable class of product-type systems of difference equations on the complex domain and a new method for proving the solvability [PDF]

Electronic Journal of Qualitative Theory of Differential Equations, 2016
This paper continues the investigation of solvability of product-type systems of difference equations, by studying the following system with two variables: $$z_n=\alpha z_{n-1}^aw_{n-2}^b,\quad w_n=\beta w_{n-3}^cz_{n-2}^d,\quad n\in\mathbb{N}_0,$$ where
Stevo Stevic
doaj   +2 more sources

On a solvable system of rational difference equations of higher order

TURKISH JOURNAL OF MATHEMATICS, 2021
Summary: In this paper, we present that the following system of difference equations \[ x_n = \frac{x_{n-k}z_{n-l}}{b_nx_{n-k}+a_nz_{n-k-l}},\; y_n=\frac{y_{n-k}x_{n-l}}{d_ny_{n-k}+c_nx_{n-k-l}},\; z_n=\frac{z_{n-k}y_{n-l}}{f_nz_{n-k}+e_ny_{n-k-l}}, \] where \(n\in \mathbb{N}_0\), \(k, l\in\mathbb{N}\), the initial values \(x_{-i}\), \(y_{-i}\), \(z_ ...
Kara, Merve, Yazlık, Yasin
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A detailed study on a solvable system related to the linear fractional difference equation [PDF]

Mathematical Biosciences and Engineering, 2021
Dans cet article, nous présentons une étude détaillée du système d'équations de différence suivant $ \begin{equation*} x_{n+1} = \frac{a}{1+y_{n}x_{n-1}}, \ y_{n+1} = \frac{b}{1+x_{n}y_{n-1}}, \ n\in\mathbb{N}_{0}, \end{equation*} $ où les paramètres $ a $ , $ b $ , et les valeurs initiales $ x_{-1}, \ ; x_{0}, \ y_{-1}, \ ; y_{0} $ sont des nombres ...
Durhasan Turgut Tollu, İbrahim Yalçınkaya, Hijaz Ahmad, Shao-Wen Yao   +3 more
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First-order product-type systems of difference equations solvable in closed form

Electronic Journal of Differential Equations, 2015
We show that the first-order system of difference equations $$ z_{n+1}=\alpha z_n^aw_n^b,\quad w_{n+1}=\beta z_n^cw_n^d,\quad n\in\mathbb{N}_0, $$ where $a,b,c,d\in\mathbb{Z}$, $\alpha,\beta \in\mathbb{C}\setminus\{0\}$, $z_0, w_0\in\mathbb{C ...
Stevo Stevic
doaj   +1 more source

The theory behind solvability of some difference equations and systems

Journal of Inequalities and Applications
Quite recently in the paper ‘Qualitative behavior of higher-order rational difference systems: positivity, asymptotic behavior, and periodicity’ (J. Inequal. Appl.
Stevo Stević
doaj   +2 more sources

On Some Solvable Difference Equations and Systems of Difference Equations [PDF]

Abstract and Applied Analysis, 2012
Here, we give explicit formulae for solutions of some systems of difference equations, which extend some very particular recent results in the literature and give natural explanations for them, which were omitted in the previous literature.
Stević, Stevo, Diblík, Josef, Iričanin, Bratislav, Šmarda, Zdeněk   +3 more
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On a two-dimensional nonlinear system of difference equations close to the bilinear system [PDF]

, 2023
We consider the two-dimensional nonlinear system of difference equations xn = xn-k ayn-l + byn-(k+l) cyn-l + dyn-(k+l) , yn = yn-k & alpha;xn-l + & beta;xn-(k+l) , & gamma;xn-l + & delta;xn-(k+l) for n E N0, where the delays k and l are two natural ...
Durhasan Turgut Tollu, Stevic, Stevo, Tollu, Durhasan Turgut, Stevo Stević   +3 more
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Solution of a Solvable System of Difference Equation

Ikonion Journal of Mathematics, 2022
In this study we give solutions for the following difference equation sytem x_{n+1}= (a.x_{n}y_{n-3}/y_{n-2}-\alpha)+\beta y_{n+1}=(b.x_{n-3}y_{n}/x_{n-2}-\beta) +\alpha n ∈N0 where the parameters a,b,, and initial values x_{-i}, y_{-i}, i=0,1,2,3 are non-zero real numbers. We show the asymptotic behavior of the system of equation.
GELİŞKEN, Ali, ARI, Murat
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