Abstract
Consider the periodic solutions of autonomous Hamiltonian systems x ˙ = J ∇ H ( x ) on the given compact energy hypersurface Σ = H −1 ( 1 ) . If Σ is convex or star-shaped, there have been many remarkable contributions for existence and multiplicity of periodic solutions. It is a hard problem to discuss the multiplicity on general hypersurfaces of contact type. In this paper we prove a multiplicity result for periodic solutions on a special class of hypersurfaces of contact type more general than star-shaped ones.
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