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 equationsxn=max{f1(xn-k1,n), ⋯,fm(xn-km,n),xn-s}, n∈N0,andxn=minf1(xn- k1,n),⋯,fm(xn-km, n),xn-s,n∈N0,where 1≤k1<⋯< km,m,s∈N, and where the functions fi:(0,∞) ×N0→(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.