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

Xiangjin Xu

doi:10.3934/dcdsb.2003.3.643

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2003, Volume 3, Issue 4: 643-654. Doi: 10.3934/dcdsb.2003.3.643

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

Xiangjin Xu^1,

1.
Department of Mathematics, Johns Hopkins Univeresity, Baltimore, MD 21218

Received: August 31, 2002

Revised: January 31, 2003

Published: October 2003

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Abstract

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.

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Mathematics Subject Classification: 37J45, 34C25, 47J30.

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