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

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

Xiangjin Xu 1,

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.
Keywords: asymptotic behaviors., Sub-harmonics, Hamiltonian system.
Mathematics Subject Classification: 37J45, 34C25, 47J3.
Citation: Xiangjin Xu. Sub-harmonics of first order Hamiltonian systems and their asymptotic behaviors. Discrete and Continuous Dynamical Systems - B, 2003, 3 (4) : 643-654. doi: 10.3934/dcdsb.2003.3.643
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