THE EXISTENCE OF PERIODIC AND SUBHARMONIC SOLUTIONS OF SUBQUADRATIC SECOND ORDER DIFFERENCE EQUATIONS

Abstract

By critical point theory, a new approach is provided to study the existence of periodic and subharmonic solutions of the second order difference equation Δ 2 x n - 1 + f ( n , x n ) = 0 , where f ∈ C(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.