Authors: Stević, Stevo 
El-Sayed Ahmed, A.
Iričanin, Bratislav
Kosmala, Witold
Affiliations: Mathematics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Higher order difference equations with homogeneous governing functions nonincreasing in each variable with unbounded solutions
Journal: Journal of Inequalities and Applications
Volume: 2022
Issue: 1
First page: 81
Issue Date: 2022
Rank: ~M21a
ISSN: 1029-242X
DOI: 10.1186/s13660-022-02811-2
By using a comparison method and some difference inequalities we show that the following higher order difference equation xn+k=1f(xn+k−1,…,xn),n∈N, where k∈ N, f: [0 , + ∞) k→ [0 , + ∞) is a homogeneous function of order strictly bigger than one, which is nondecreasing in each variable and satisfies some additional conditions, has unbounded solutions, presenting a large class of such equations. The class can be used as a useful counterexample in dealing with the boundedness character of solutions to some difference equations. Some analyses related to such equations and a global convergence result are also given.
Keywords: Difference equation | Homogeneous function | Unbounded solutions
Publisher: Springer Link

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