El-Sayed Ahmed, A.
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||Abstract:||
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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checked on Mar 26, 2023
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