By critical point theory, a new approach is provided to study the existence of periodic and subharmonic solutions of the second order difference equation



where fC(R × Rm, Rm), f(t+M,z)+f(t,z) for any (t, z)∈R × Rm 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.

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