Some results on connecting orbits for a class of Hamiltonian systems (Q1812935)

The existence of various kinds of connecting orbits is established for the Hamiltonian system \((HS)\quad q''+V'(q)=0\) as well as its time periodic analogue. For the autonomous case, the main assumption is that V has a global maximum, e.g. at \(x=0\). Variational methods then establish the existence of various kinds of orbits terminating at \(x=0\). For the time dependent case it is assumed that V has a local but not global maximum at \(x=0\) and it is proved that (HS) has a homoclinic orbit emanating from and terminating at 0.