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

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  • 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.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.


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