Title: Homoclinic orbits for superlinear Hamiltonian systems without Ambrosetti-Rabinowitz growth condition
Abstract: In this paper we prove the existence of homoclinic orbits for thefirst order non-autonomous Hamiltonian system$\dot{z}=\mathcal {J}H_{z}(t,z),$where $H(t,z)$ depends periodically on $t$. We establish someexistence results of the homoclinic orbits for weak superlinearcases. To this purpose, we apply a new linking theorem to providebounded Palais-Samle sequences.