# American Institute of Mathematical Sciences

November  2003, 3(4): 643-654. doi: 10.3934/dcdsb.2003.3.643

## Sub-harmonics of first order Hamiltonian systems and their asymptotic behaviors

 1 Department of Mathematics, Johns Hopkins Univeresity, Baltimore, MD 21218, United States

Received  September 2002 Revised  February 2003 Published  August 2003

In this paper some new existence results for sub-harmonics are proved for first order Hamiltonian systems with super-quadratic potentials by using two new estimates on $C^0$ bound for the periodic solutions. Applying the uniform estimates on the sub-harmonics, the asymptotic behaviors of sub-harmonics is studied when the systems have globally super-quadratic potentials.
Citation: Xiangjin Xu. Sub-harmonics of first order Hamiltonian systems and their asymptotic behaviors. Discrete & Continuous Dynamical Systems - B, 2003, 3 (4) : 643-654. doi: 10.3934/dcdsb.2003.3.643
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