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 ?0?and ?1,then for any ??(?O,?1),there is a solu-tion whose rotation number is ?.So the problem we need to solve is to construct such a solution with rotation number ?.We first construct a supersolution and a subsolution with rotation number?,then use the theory of supersolutions and subsotions to obtain a solution that satisfies the conditions.