Results 11 to 20 of about 2,105 (253)
Symmetric nonlinear solvable system of difference equations [PDF]
Electronic Journal of Qualitative Theory of Differential EquationsWe show the theoretical solvability of the system of difference equations $$x_{n+k}=\frac{y_{n+l}y_n-cd}{y_{n+l}+y_n-c-d},\quad y_{n+k}=\frac{x_{n+l}x_n-cd}{x_{n+l}+x_n-c-d},\quad n\in\mathbb{N}_0,$$ where $k\in\mathbb{N}$, $l\in\mathbb{N}_0 ...
Stevo Stevic +2 more
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On a solvable system of difference equations of sixth-order
Miskolc Mathematical Notes, 2023 In this paper, we study the following two-dimesional system of difference equations (Formula presented.), (Formula presented.), n ? N0; where the parameters a,b,c,d and the initial values x-i,y-i, i ? {1,2,3,4,5,6}, are real numbers. We show that some subclasses of nonlinear two-dimensional system of difference equations are solvable in closed form. We
Karakaya, Dilek +2 more
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On a solvable three-dimensional system of difference equations [PDF]
Filomat, 2020 In this paper, we show that the following three-dimensional system of difference equations xn = zn-2xn-3/axn-3 + byn-1, yn = xn-2yn-3/cyn-3 + dzn-1, zn = yn-2zn-3/ezn-3+ fxn-1, n ? N0, where the parameters a, b, c, d, e, f and the initial values x-i, y-i, z-i, i ? {1, 2, 3}, are real numbers, can be solved, extending further some results in
Kara, Merve, Yazlık, Yasin
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A solvable system of difference equations [PDF]
, 2020 Summary: In this paper, we show that the system of difference equations \[x_n={\frac{ay^p_{n-1}+b(x_{n-2}y_{n-1})^{p-1}}{cy_{n-1}+dx^{p-1}_{n-2}}},\ y_n={\frac{{\alpha}x^p_{n-1}+{\beta}(y_{n-2}x_{n-1})^{p-1}}{{\gamma}x_{n-1}+{\delta}y^{p-1}_{n-2}}}, \] \(n\in \mathbb{N}_0\) where the parameters \(a, b, c, d, \alpha, \beta, \gamma, \delta, p\) and the ...
Taskara, Necati. +3 more
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General k-Dimensional Solvable Systems of Difference Equations [PDF]
Symmetry, 2017 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.
Stevo Stević
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On a solvable difference equations system
FilomatIn this paper, we study three dimensional system of difference equations. Firstly, we examine the solutions of the mentioned system depending on whether the parameters are equal to zero or non-zero. In addition, the solutions of this system are obtained in closed form.
Ömer Aktaş, Merve Kara, Yasin Yazlik
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On a practically solvable product-type system of difference equations of second order [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2016 The problem of solvability of the following second order system of difference equations $$z_{n+1}=\alpha z_n^aw_n^b,\qquad w_{n+1}=\beta w_n^cz_{n-1}^d,\qquad n\in\mathbb{N}_0,$$ where $a,b,c,d\in\mathbb{Z}$, $\alpha, \beta \in\mathbb{C}\setminus\{0\}$, $
Stevo Stevic, Dragana Rankovic
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Explicit Solutions of a Three-dimensional System of Nonlinear Difference Equations [PDF]
Hittite Journal of Science and Engineering, 2018 I n this paper, we show that the system of difference equations 1 11 0 , , , N , 111 n n nn nn n nn n n n n n n xy yz zx xyz n xy yz zx + ++ + ++ = = = ∈ +++ where the initial values xyz , , are real numbers, are solvable in explicit form via ...
Durhasan Turgut Tollu +1 more
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Solvable product-type system of difference equations whose associated polynomial is of the fourth order [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2017 The solvability problem for the following system of difference equations $$z_{n+1}=\alpha z_n^aw_n^b,\quad w_{n+1}=\beta w_{n-1}^cz_{n-2}^d,\quad n\in\mathbb{N}_0,$$ where $a,b,c,d\in\mathbb{Z}$, $\alpha,\beta\in\mathbb{C}\setminus\{0\}$, $z_{-2}, z_{-1}
Stevo Stevic
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Solvable product-type system of difference equations of second order
Electronic Journal of Differential Equations, 2015 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 ...
Stevo Stevic +3 more
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