On a Max Difference Equation

In this paper we study the existence of generalized invariants and the periodicity of the positive solutions of max equations, xn+1 = max an n i=n−k+1 xi bn n i=n−k xi n= 0 1 where an bn are sequences of positive numbers, x−k x−k+1 x0 ∈ 0 ∞ and k ∈ 2 3 .