Abstract
In this paper new estimates on the C0-norm of solutions are shown for first order convex Hamiltonian systems possessing super-quadratic potentials. Applying these estimates, some new results on the existence of subharmonics are obtained, which generalize the main results in Ekeland and Hofer [5], and a question about a priori estimates on subharmonics raised by Ekeland and Hofer [5] is answered when the convex Hamiltonian systems have globally super-quadratic potentials. Using the uniform estimates on the subharmonics, the behavior of convergence of subharmonics is studied too.
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