Periodicity of a class of nonautonomous max-type difference equations

Abstract In this note we prove several general and easily applicable results regarding the periodicity of positive solutions of the following difference equations x n = max { f 1 ( x n - k 1 , n ) , … , f m ( x n - k m , n ) , x n - s } , n ∈ N 0 , and x n = min f 1 ( x n - k 1 , n ) , … , f m ( x n - k m , n ) , x n - s , n ∈ N 0 , where 1 ⩽ k 1 ⋯ k m , m , s ∈ N , and where the functions f i : ( 0 , ∞ ) × N 0 → ( 0 , ∞ ) , 1 ⩽ i ⩽ m , satisfy some additional conditions. These results considerably extend and unify numerous results on max-type difference equations existing in the literature.

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