Solvable product-type system of difference equations of second order
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 solvable in closed form, and present a method for...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2015-06-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2015/169/abstr.html |
| _version_ | 1818869992024702976 |
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| author | Stevo Stevic Mohammed A. Alghamdi Abdullah Alotaibi Elsayed M. Elsayed |
| author_facet | Stevo Stevic Mohammed A. Alghamdi Abdullah Alotaibi Elsayed M. Elsayed |
| author_sort | Stevo Stevic |
| collection | DOAJ |
| description | 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 solvable in closed form, and present a method for finding its solutions. |
| first_indexed | 2024-12-19T11:59:56Z |
| format | Article |
| id | doaj.art-b710b450cb2c463099aad2f52eae4131 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-19T11:59:56Z |
| publishDate | 2015-06-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-b710b450cb2c463099aad2f52eae41312022-12-21T20:22:31ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912015-06-012015169,120Solvable product-type system of difference equations of second orderStevo Stevic0Mohammed A. Alghamdi1Abdullah Alotaibi2Elsayed M. Elsayed3 Serbian Academy of Sciences, Beograd, Serbia King Abdulaziz Univ. Jeddah, Saudi Arabia King Abdulaziz Univ. Jeddah, Saudi Arabia King Abdulaziz Univ. Jeddah, Saudi Arabia 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 solvable in closed form, and present a method for finding its solutions.http://ejde.math.txstate.edu/Volumes/2015/169/abstr.htmlSolvable system of difference equationssecond-order systemproduct-type systemlong-term behavior |
| spellingShingle | Stevo Stevic Mohammed A. Alghamdi Abdullah Alotaibi Elsayed M. Elsayed Solvable product-type system of difference equations of second order Electronic Journal of Differential Equations Solvable system of difference equations second-order system product-type system long-term behavior |
| title | Solvable product-type system of difference equations of second order |
| title_full | Solvable product-type system of difference equations of second order |
| title_fullStr | Solvable product-type system of difference equations of second order |
| title_full_unstemmed | Solvable product-type system of difference equations of second order |
| title_short | Solvable product-type system of difference equations of second order |
| title_sort | solvable product type system of difference equations of second order |
| topic | Solvable system of difference equations second-order system product-type system long-term behavior |
| url | http://ejde.math.txstate.edu/Volumes/2015/169/abstr.html |
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