Existence and multiplicity results for heteroclinic orbits of second order Hamiltonian systems
For a non-autonomous Hamiltonian system of the form \(\ddot q-V' (t,q)=0\) the existence of heteroclinic orbits is discussed. The potential \(V\) does not need to be periodic or quasiperiodic, it is only assumed that there exist finitely or infinitely many points which minimize \(V\) at any fixed time. It is possible to show the existence of heteroclinic orbits between pairs of these minimizers using a penalization technique. This method combined with a mountain pass type theorem allows to show the existence of multiple heteroclinic connections between pairs of equilibria.
scientific article; zbMATH DE number 1384453