Symmetric nonlinear solvable system of difference equations
We 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 $k\in\mathbb{N}$, $l\in\mathbb{N}_0$, $l<k$, $c, d\in\mathbb{C}$ and $x_j, y_j\in\mathbb{C}...
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| Format: | Article |
| Language: | English |
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University of Szeged
2024-09-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11195 |
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| author | Stevo Stevic Bratislav Iricanin Witold Kosmala |
| author_facet | Stevo Stevic Bratislav Iricanin Witold Kosmala |
| author_sort | Stevo Stevic |
| collection | DOAJ |
| description | We 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 $k\in\mathbb{N}$, $l\in\mathbb{N}_0$, $l<k$, $c, d\in\mathbb{C}$ and $x_j, y_j\in\mathbb{C}$, $j=\overline{0,k-1}$. For several special cases of the system, we give some detailed explanations on how some formulas for their general solutions can be found in closed form, that is, we show their practical solvability. To do this, among other things, we use the theory of homogeneous linear difference equations with constant coefficients and the product-type difference equations with integer exponents, which are theoretically solvable. |
| format | Article |
| id | doaj-art-cfe40bcba853441c8e3cdd8a7ba388ea |
| institution | DOAJ |
| issn | 1417-3875 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj-art-cfe40bcba853441c8e3cdd8a7ba388ea2025-08-20T02:42:30ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752024-09-0120244911610.14232/ejqtde.2024.1.4911195Symmetric nonlinear solvable system of difference equationsStevo Stevic0https://orcid.org/0000-0002-7202-9764Bratislav Iricaninhttps://orcid.org/0000-0001-7457-7716Witold Kosmala1https://orcid.org/0000-0002-2101-9224Mathematical Institute of the Serbian Academy of Sciences, Beograd, SerbiaFaculty of Electrical Engineering, Belgrade University, Belgrade, SerbiaWe 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 $k\in\mathbb{N}$, $l\in\mathbb{N}_0$, $l<k$, $c, d\in\mathbb{C}$ and $x_j, y_j\in\mathbb{C}$, $j=\overline{0,k-1}$. For several special cases of the system, we give some detailed explanations on how some formulas for their general solutions can be found in closed form, that is, we show their practical solvability. To do this, among other things, we use the theory of homogeneous linear difference equations with constant coefficients and the product-type difference equations with integer exponents, which are theoretically solvable.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11195symmetric system of difference equationssolvable systemsolution in closed form |
| spellingShingle | Stevo Stevic Bratislav Iricanin Witold Kosmala Symmetric nonlinear solvable system of difference equations Electronic Journal of Qualitative Theory of Differential Equations symmetric system of difference equations solvable system solution in closed form |
| title | Symmetric nonlinear solvable system of difference equations |
| title_full | Symmetric nonlinear solvable system of difference equations |
| title_fullStr | Symmetric nonlinear solvable system of difference equations |
| title_full_unstemmed | Symmetric nonlinear solvable system of difference equations |
| title_short | Symmetric nonlinear solvable system of difference equations |
| title_sort | symmetric nonlinear solvable system of difference equations |
| topic | symmetric system of difference equations solvable system solution in closed form |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11195 |
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