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

Jun Wang; Junxiang Xu; Fubao Zhang

doi:10.3934/dcds.2010.27.1241

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2010, Volume 27, Issue 3: 1241-1257. Doi: 10.3934/dcds.2010.27.1241

This issue Previous Article On the spatial asymptotics of solutions of the Toda lattice Next Article Preface

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

1.
Department of Mathematics, Southeast University, Nanjing 210096

Received: August 31, 2009

Revised: December 31, 2009

Published: August 2010

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Abstract

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: 53C35.

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

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