New class of practically solvable systems of difference equations of hyperbolic-cotangent-type
The systems of difference equations $$x_{n+1}=\frac{u_nv_{n-2}+a}{u_n+v_{n-2}},\quad y_{n+1}=\frac{w_ns_{n-2}+a}{w_n+s_{n-2}},\quad n\in\mathbb{N}_0,$$ where $a, u_0, w_0, v_j, s_j$ $j=-2,-1,0,$ are complex numbers, and the sequences $u_n$, $v_n,$ $w_n$, $s_n$ are $x_n$ or $y_n$, are studied. It is...
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| Format: | Article |
| Language: | English |
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University of Szeged
2020-12-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8931 |
| _version_ | 1797830493823041536 |
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| author | Stevo Stevic |
| author_facet | Stevo Stevic |
| author_sort | Stevo Stevic |
| collection | DOAJ |
| description | The systems of difference equations
$$x_{n+1}=\frac{u_nv_{n-2}+a}{u_n+v_{n-2}},\quad y_{n+1}=\frac{w_ns_{n-2}+a}{w_n+s_{n-2}},\quad n\in\mathbb{N}_0,$$ where $a, u_0, w_0, v_j, s_j$ $j=-2,-1,0,$ are complex numbers, and the sequences $u_n$, $v_n,$ $w_n$, $s_n$ are $x_n$ or $y_n$, are studied. It is shown that each of these sixteen systems is practically solvable, complementing some recent results on solvability of related systems of difference equations. |
| first_indexed | 2024-04-09T13:37:00Z |
| format | Article |
| id | doaj.art-26c043064ca9445ab82ebe5870d24ee4 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:37:00Z |
| publishDate | 2020-12-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-26c043064ca9445ab82ebe5870d24ee42023-05-09T07:53:10ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752020-12-0120208912510.14232/ejqtde.2020.1.898931New class of practically solvable systems of difference equations of hyperbolic-cotangent-typeStevo Stevic0Mathematical Institute of the Serbian Academy of Sciences, Beograd, Serbia & Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan, Republic of ChinaThe systems of difference equations $$x_{n+1}=\frac{u_nv_{n-2}+a}{u_n+v_{n-2}},\quad y_{n+1}=\frac{w_ns_{n-2}+a}{w_n+s_{n-2}},\quad n\in\mathbb{N}_0,$$ where $a, u_0, w_0, v_j, s_j$ $j=-2,-1,0,$ are complex numbers, and the sequences $u_n$, $v_n,$ $w_n$, $s_n$ are $x_n$ or $y_n$, are studied. It is shown that each of these sixteen systems is practically solvable, complementing some recent results on solvability of related systems of difference equations.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8931system of difference equationsgeneral solutionsolvability of difference equationshyperbolic-cotangent-type system of difference equations |
| spellingShingle | Stevo Stevic New class of practically solvable systems of difference equations of hyperbolic-cotangent-type Electronic Journal of Qualitative Theory of Differential Equations system of difference equations general solution solvability of difference equations hyperbolic-cotangent-type system of difference equations |
| title | New class of practically solvable systems of difference equations of hyperbolic-cotangent-type |
| title_full | New class of practically solvable systems of difference equations of hyperbolic-cotangent-type |
| title_fullStr | New class of practically solvable systems of difference equations of hyperbolic-cotangent-type |
| title_full_unstemmed | New class of practically solvable systems of difference equations of hyperbolic-cotangent-type |
| title_short | New class of practically solvable systems of difference equations of hyperbolic-cotangent-type |
| title_sort | new class of practically solvable systems of difference equations of hyperbolic cotangent type |
| topic | system of difference equations general solution solvability of difference equations hyperbolic-cotangent-type system of difference equations |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8931 |
| work_keys_str_mv | AT stevostevic newclassofpracticallysolvablesystemsofdifferenceequationsofhyperboliccotangenttype |