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Periodicity of a class of nonautonomous max-type difference equations. (English) Zbl 1225.39018

The paper contains new unifying periodicity criteria for the following difference equations

x n =maxf 1 (x n-k 1 ,n),...,f m (x n-k m ,n),x n-s ,n 0

with 1k 1 <<k m , m,s, then for

x n =minf 1 (x n-k 1 ,n),,f m (x n-k m ,n),x n-s ,n 0

with 1k 1 <<k m , m,s and finally for

x n =maxf 1 (x n-k 1 (1) ,,x n-k t 1 (1) ),,f m (x n-k 1 (m) ,,x n-k t m (m) ),x n-s ,n 0

with m,s, t i , i=1,,m, 1k 1 (i) <<k t i (i) , i=1,,m.

The assumptions are various monotonicity and periodicity conditions for the right hand side of the considered equations.

MSC:
39A23Periodic solutions (difference equations)
39A20Generalized difference equations
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