Positive periodic solutions of nonlinear functional difference equations depending on a parameter

In this paper, we use the upper and lower solutions method to show that there existsa λ*, such that the nonlinear functional difference equation of the form χ(n + 1) = a(n)χ(n) + λh(n)ƒ(χ(n − τ(n))), n ε Z, has at least one positive T-periodic solutions for λ ε (0, λ* and does not have any positive T-periodic solutions for λ > λ*, where a(n), h(n), and τ(n) are T-periodic functions.