On positive periodic solutions of functional difference equations with forcing term and applications

Consider the following non-autonomous first order functional difference equation Δx(n)=a(n)x(n)−λh(n)f(n,x(n),x(n−τ1(n)),…,x(n−τm(n)))+r(n),n∈Z. It is shown that, under certain assumptions, there exist positive periodic solutions. Applications are given to illustrate the main results.