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

Pages: 1241 - 1257, Volume 27, Issue 3, July 2010

doi:10.3934/dcds.2010.27.1241       Abstract        Full Text (248.8K)       Related Articles

Jun Wang - Department of Mathematics, Southeast University, Nanjing 210096, China (email)
Junxiang Xu - Department of Mathematics, Southeast University, Nanjing 210096, China (email)
Fubao Zhang - Department of Mathematics, Southeast University, Nanjing 210096, China (email)

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.

Received: September 2009;      Revised: January 2010;      Published: March 2010.