# American Institute of Mathematical Sciences

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

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

 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.

Citation: Jun Wang, Junxiang Xu, Fubao Zhang. Homoclinic orbits for superlinear Hamiltonian systems without Ambrosetti-Rabinowitz growth condition. Discrete and Continuous Dynamical Systems, 2010, 27 (3) : 1241-1257. doi: 10.3934/dcds.2010.27.1241
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