On the minimal periodic solutions of nonconvex superlinear Hamiltonian systems

This paper proves a multiplicity result for the minimal periodic solutions of Hamiltonian system ˙x(t) = J∇H(x(t)) under a superquadratic hypothesis on H weaker than the Ambrosetti–Rabinowitz-type condition. We also define a class of homogeneous functions, that are more general than the classical ones, and prove the Rabinowitz’s conjecture in the case of H satisfying such new homogeneity. © 2006 Elsevier Inc. All rights reserved.