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August  2010, 27(3): 1241-1257. doi: 10.3934/dcds.2010.27.1241

Homoclinic orbits for superlinear Hamiltonian systems without Ambrosetti-Rabinowitz growth condition

Jun Wang 1, , Junxiang Xu 1, and  Fubao Zhang 1,

1. 

Department of Mathematics, Southeast University, Nanjing 210096, China, China, China

Received  September 2009 Revised  January 2010 Published  March 2010

In this paper we prove the existence of homoclinic orbits for the first order non-autonomous Hamiltonian system

$\dot{z}=\mathcal {J}H_{z}(t,z),$

where $H(t,z)$ depends periodically on $t$. We establish some existence results of the homoclinic orbits for weak superlinear cases. To this purpose, we apply a new linking theorem to provide bounded Palais-Samle sequences.

Keywords: Homoclinic orbits; Hamiltonian systems; Linking theorem; Variational methods..
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
Citation: Jun Wang, Junxiang Xu, Fubao Zhang. Homoclinic orbits for superlinear Hamiltonian systems without Ambrosetti-Rabinowitz growth condition. Discrete & Continuous Dynamical Systems, 2010, 27 (3) : 1241-1257. doi: 10.3934/dcds.2010.27.1241
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