Periodic solutions in totally nonlinear difference equations with functional delay.

We use the modification of Krasnoselskii's fixed point theorem due to T. A. Burton ( [1] Theorem 3) to show that the totally nonlinear difference equation with functional delay Δx (t) = -a (t) x³ (t + 1) + G (t, x³ (t), x³ (t - g (t))), ∀t ϵ ℤ, has periodic solutions. We invert this equation to construct a sum of a compact map and a large contraction which is suitable for applying Krasnoselskii-Burton theorem. Finally, an example is given to illustrate our result. [ABSTRACT FROM AUTHOR]