Abstract
This paper studies the stability of the periodic solutions of the second order Hamiltonian systems with even superquadratic or subquadratic potentials. The author proves that in the subquadratic case, there exist infinite geometrically distinct elliptic periodic solutions, and in the superquadratic case, there exist infinite geometrically distinct periodic solutions with at most one instability direction if they are half period non-degenerate, otherwise they are elliptic.
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