The Existence of Periodic and Subharmonic Solutions of Subquadratic Second Order Difference Equations

By critical point theory, a new approach is provided to study the existence of periodic and subharmonic solutions of the second order difference equationΔ 2 x n ‐ 1 + f ( n , x n ) = 0 ,where f ∈ C (R × R m , R m ), f ( t + M , z )+ f ( t , z ) for any ( t, z )∈R × R m and M is a positive integer. This is probably the first time critical point theory has been applied to deal with the existence of periodic solutions of difference systems.