Quasi-periodic Monotone Recurrence Relations

We study the existence of solutions with rotation numbers for quasi-periodic mono-tone recurrence relations.In this paper,we give a sufficient condition.If quasi-periodic monotone recurrence relations have a strict supersolution and a strict subsolution which exchange their rotation numbers ω0、and ω1,then for any ω∈(ωO,ω1),there is a solu-tion whose rotation number is ω.So the problem we need to solve is to construct such a solution with rotation number ω.We first construct a supersolution and a subsolution with rotation numberω,then use the theory of supersolutions and subsotions to obtain a solution that satisfies the conditions.