Homoclinics for strongly indefinite almost periodic second order Hamiltonian systems

Under certain assumptions, we prove the existence of homoclinic solutions for almost periodic second order Hamiltonian systems in the strongly indefinite case. The proof relies on a careful analysis of the energy functional restricted to the generalized Nehari manifold, and the existence and fine properties of special Palais-Smale sequences. © 2019 Walter de Gruyter GmbH, Berlin/Boston 2019.