Existence of positive solutions for first order discrete periodic boundary value problems with delay

Let T>3T>3 be a positive integer and T={0,1,2,…,T−1}T={0,1,2,…,T−1}. We prove the existence of positive periodic solutions of the nonlinear discrete boundary value problem Δu(t)=a(t)g(u(t))u(t)−λb(t)f(u(t−τ(t))),t∈T,u(0)=u(T). Our approach is based upon the global bifurcation techniques.