Existence of positive solutions of PBVPs for first-order difference equations

We consider the existence of positive solutions for the following first-order periodic boundary value problem: x(n+1)=x(n)−f(n,x(n)), 0≤n≤ω−1, x(0)=x(ω). Some criteria for existence of positive solutions of the above difference boundary problem are established by using Krasnosel'skiĭ's fixed point theorem, and some multiplicity results of positive solutions are also derived