Homoclinic orbits for a class of singular second order Hamiltonian systems in ? ~3

摘要

We consider a conservative second order Hamiltonian system in ? ~3 with a potential V having a global maximum at the origin and a line l ∩ {0} = θ{symbol} as a set of singular points. Under a certain compactness condition on V at infinity and a strong force condition at singular points we study, by the use of variational methods and geometrical arguments, the existence of homoclinic solutions of the system.