Subharmonics for First Order Convex Nonautonomous Hamiltonian Systems

In this paper new estimates on the C ⁰-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.