Existence of periodic solutions for fourth-order difference equations
The authors consider the fourth-order difference equation, Delta 2(r(n-2)Delta(2)x(n-2)) + f(n,x(n)) = 0, n is an element of Z, where f : Z x R -> R is a continuous function in the second variable, f (n + T, z) = f (n, z), r(n+T) = r(n), for all (n, z) is an element of Z x 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. (c) 2005 Elsevier Ltd. All rights reserved.
periodic solution linking theorem nonlinear difference equations critical point theory variational structure