Existence of periodic solutions for fourth-order difference equations

The authors consider the fourth-order difference equation, Δ2(rn−2Δ2xn−2)+f(n,xn)=0,n Z, 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.