Unbounded Solutions of the Difference Equation xn=xn−lxn−k−1
The following difference equation xn=xn−lxn−k−1, n∈ℕ0, where k,l∈ℕ, k<l, gcd(k,l)=1, and the initial values x-l,…,x-2,x-1 are real numbers, has been investigated so far only for some particular values of k and l. To get any general result on the equation is turned out as a not so easy problem. In...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/561682 |
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| _version_ | 1832565155740778496 |
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| author | Stevo Stević Bratislav Iričanin |
| author_facet | Stevo Stević Bratislav Iričanin |
| author_sort | Stevo Stević |
| collection | DOAJ |
| description | The following difference equation
xn=xn−lxn−k−1, n∈ℕ0,
where k,l∈ℕ, k<l, gcd(k,l)=1, and the initial values x-l,…,x-2,x-1 are
real numbers, has been investigated so far only for some particular values of k
and l. To get any general result on the equation is turned out as a not so easy
problem. In this paper, we give the first result on the behaviour of solutions of the
difference equation of general character, by describing the long-term behavior
of the solutions of the equation for all values of parameters k and l, where
the initial values satisfy the following condition min{x-l,…,x-2,x-1}. |
| format | Article |
| id | doaj-art-3db22409d44d442bb1ca033699142246 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-3db22409d44d442bb1ca0336991422462025-02-03T01:09:09ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/561682561682Unbounded Solutions of the Difference Equation xn=xn−lxn−k−1Stevo Stević0Bratislav Iričanin1Mathematical Institute of the Serbian Academy of Sciences and Arts, Knez Mihailova 36/III, 11000 Beograd, SerbiaFaculty of Electrical Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, Belgrade 11120, SerbiaThe following difference equation xn=xn−lxn−k−1, n∈ℕ0, where k,l∈ℕ, k<l, gcd(k,l)=1, and the initial values x-l,…,x-2,x-1 are real numbers, has been investigated so far only for some particular values of k and l. To get any general result on the equation is turned out as a not so easy problem. In this paper, we give the first result on the behaviour of solutions of the difference equation of general character, by describing the long-term behavior of the solutions of the equation for all values of parameters k and l, where the initial values satisfy the following condition min{x-l,…,x-2,x-1}.http://dx.doi.org/10.1155/2011/561682 |
| spellingShingle | Stevo Stević Bratislav Iričanin Unbounded Solutions of the Difference Equation xn=xn−lxn−k−1 Abstract and Applied Analysis |
| title | Unbounded Solutions of the Difference Equation xn=xn−lxn−k−1 |
| title_full | Unbounded Solutions of the Difference Equation xn=xn−lxn−k−1 |
| title_fullStr | Unbounded Solutions of the Difference Equation xn=xn−lxn−k−1 |
| title_full_unstemmed | Unbounded Solutions of the Difference Equation xn=xn−lxn−k−1 |
| title_short | Unbounded Solutions of the Difference Equation xn=xn−lxn−k−1 |
| title_sort | unbounded solutions of the difference equation xn xn lxn k 1 |
| url | http://dx.doi.org/10.1155/2011/561682 |
| work_keys_str_mv | AT stevostevic unboundedsolutionsofthedifferenceequationxnxnlxnk1 AT bratislaviricanin unboundedsolutionsofthedifferenceequationxnxnlxnk1 |