Authors: Stević, Stevo 
Iričanin, Bratislav
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Unbounded solutions of the difference equation xn = x n-Lx-k-1
Journal: Abstract and Applied Analysis
Volume: 2011
Issue Date: 25-Nov-2011
Rank: M21a
ISSN: 1085-3375
DOI: 10.1155/2011/561682
Abstract: 
The following difference equation xn = x n - l x n - k- 1, n € ℕ0, where k, l ,€ ℕk < 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 }. Copyright
Publisher: Hindawi
Project: Modulation of intracellular energy balance-controlling signalling pathways in therapy of cancer and neuro-immuno-endocrine disorders 
Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education 
Physical and functional effects of radiation interaction with electrotechnical and biological systems 

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