Existence of periodic solutions for fourth-order difference equations

where f : Z × R → R is a continuous function in the second variable, f(n + T, z) = f(n, z), rn+T = rn, for all (n, z) ∈ Z × R, and T is a positive integer. By using linking theorem, the authors obtain some new criteria for the existence and multiplicity of periodic solutions of the fourth-order difference equation.